What are they?
From Wikipedia: A mycorrhiza (from Greek μύκης mýkēs, “fungus”, and ῥίζα rhiza, “root”; pl. mycorrhizae, mycorrhiza or mycorrhizas) is a mutual symbiotic association between a fungus and a plant. The fungus colonizes the host plant’s root tissues, either intracellularly as in arbuscular mycorrhizal fungi (AMF or AM) or extracellularly as in ectomycorrhizal fungi. The association is sometimes [usually] mutualistic. In particular species or in particular circumstances, mycorrhizae may have a parasitic association with host plants.The plant makes organic molecules such as sugars by photosynthesis and supplies them to the fungus, and the fungus supplies to the plant water and mineral nutrients, such as phosphorus, taken from the soil. Mycorrhizas are located in the roots of vascular plants, but mycorrhiza-like associations also occur in bryophytes and there is fossil evidence that early land plants that lacked roots formed arbuscular mycorrhizal associations. Most plant species form mycorrhizal associations, though some families like Brassicaceae and Chenopodiaceae cannot.

Related to trees From Quirk et al., 2012 (references removed): “Fossil roots of early gymnosperms from at least the Carboniferous are colonized by arbuscular mycorrhizal (AM) fungi, and this type of mycorrhiza continues to be found in the vast majority of tree species, including in most of the more recently evolved angiosperm taxa . Independently evolving ectomycorrhizal (EM) fungi diversified from the Cretaceous, forming mycorrhizal associations with the Pinaceae and angiosperm trees in the Betulaceae and Fagaceae that now dominate temperate and boreal forests, as well as with angiosperm trees in the Myrtaceae, Fabaceae and Dipterocarpaceae, that can form dominant stands in warm temperate and tropical regions. Both mycorrhizal types use host photosynthate to support extensive hyphal networks with high absorptive surface area for nutrient element mass transfer from the substrate. In trees forming AM, root functioning is augmented by the nutrientscavenging activities of the fungi, whereas EM fungi completely envelop tree root tips to subsume the soil – root interface. EM fungi thereby control the translocation of elements from soil to tree and can also enhance mineral weathering through exudation of low molecular weight organic compounds.

Types (adapted from Wikipedia)

Mycorrhizas are commonly divided into ectomycorrhizas and endomycorrhizas based on whether or not hyphae penetrate root cells.

Ectomycorrhiza – hyphae of ectomycorrhizal fungi do not penetrate individual cells within the root
Ectomycorrhizas, or EcM, are symbiotic associations between the roots of around 10% of plant families, mostly woody plants including the birch, dipterocarp, eucalyptus, oak, pine, and rose families, orchids, and fungi belonging to the Basidiomycota, Ascomycota, and Zygomycota. Ectomycorrhizas consist of a hyphal sheath, or mantle, covering the root tip and a Hartig net of hyphae surrounding the plant cells within the root cortex. An individual tree may have 15 or more different fungal EcM partners at one time.

Amanita muscaria Photo by Tony Wills

Note: many of the “mushrooms” we see in forests are the fruiting bodies of EcMs associated with trees; when you see mushrooms near the base of a tree, note both the species of mushroom and the tree species, then do a search to see if they are known to be associated. A common mycorrhizal mushroom: Amanita muscaria; it associates with pine, oak, spruce, fir, birch, and cedar. Some species of the genus Amanita ( 40+ spp in the northeast) are mycorrizal, some are purely saprophytic. Mycorrhizal species cannot live saprophytically (i.e. can not grow on dead, decomposing organic matter) – view Deadly and Delicious Amanitas Can No Longer Decompose by Jennifer Frazer in Scientific American Blog (2012); also Retracing the Roots of Fungal Symbioses (News Release from Joint Genome Institute (2015) “Mycorrhizal symbioses are highly complex, but analyses of the 49 genomes indicate that they have evolved independently in many fungal lineages.”

Endomycorrhizaehyphae of endomycorrhizal fungi penetrate the cell wall and invaginate the cell membrane
Arbuscular mycorrhiza  or AM (formerly known as vesicular-arbuscular mycorrhizas, or VAM). Arbuscular mycorrhizas are formed only by fungi in the division Glomeromycota; they are “asexual” – no fruting bodies or “mushrooms” are formed.  Arbuscular mycorrhizas are found in 85% of all plant families, and occur in many crop species.
Ericoid mycorrhiza. Ericoid mycorrhizae are the third of the three more ecologically important types. Ericoid mycorrhizal fungi establish loose hyphal networks around the outside of hair roots, from which they penetrate the walls of cortical cells to form intracellular coils that can densely pack individual plant cells. Found associated with members of the plant family Ericaceae [the heath family- e.g., blueberries] and several lineages of mycorrhizal fungi. This symbiosis represents an important adaptation to acidic and nutrient poor soils that species in the Ericaceae typically inhabit including boreal forests, bogs, and heathlands. Ericoid mycorrhizas have been shown to have considerable saprotrophic capabilities, which would enable plants to receive nutrients from not-yet-decomposed materials via the decomposing actions of their ericoid partners.
Orchid mycorrhiza Orchid mycorrhizae are symbiotic relationships between the roots of plants of the family Orchidaceae and a variety of fungi. All orchids are myco-heterotrophic at some point in their life cycle. Orchid mycorrhizae are critically important during orchid germination, as an orchid seed has virtually no energy reserve and obtains its carbon from the fungal symbiont.The symbiosis starts with a structure called a protocorm. During the symbiosis, the fungus develops structures called pelotons within the root cortex of the orchid. Many adult orchids retain their fungal symbionts throughout their life, although the benefits to the adult photosynthetic orchid and the fungus remain largely unexplained.

Endoectomycorrhiza: The Arbutoid Mycorrhizae
This type of mycorrhiza involves plants of the Ericaceae (Heath) subfamily Arbutoideae (in NS: bearberry, Arctostaphylos uvaursi). It is however different from ericoid mycorrhiza and resembles ectomycorrhiza, both functionally and in terms of the fungi involved. It differs from ectomycorrhiza in that some hyphae actually penetrate into the root cells, making this type of mycorrhiza an ectendomycorrhiza.

More on Mycorrhizal Types and their evolution
Phylogenetic distribution and evolution of mycorrhizas in land plants
B. Wang and Y.L. Qiu 2006 Mycorrhiza 16: 299–363 “A survey of 659 papers .. was conducted to compile a checklist of mycorrhizal occurrence among 3,617 species (263 families) of land plants… First, 80 and 92% of surveyed land plant species and families are mycorrhizal. Second, arbuscular mycorrhiza (AM) is the predominant and ancestral type of mycorrhiza in land plants. Its occurrence in a vast majority of land plants and early-diverging lineages of liverworts suggests that the origin of AM probably coincided with the origin of land plants. Third, ectomycorrhiza (ECM) and its derived types independently evolved from AM many times through parallel evolution. Coevolution between plant and fungal partners in ECM and its derived types has probably contributed to diversification of both plant hosts and fungal
symbionts. Fourth, mycoheterotrophy and loss of the mycorrhizal condition also evolved many times independently in land plants through parallel evolution.

Related to nutrient cycling
The mycorrhizal-associated nutrient economy: a new framework for predicting carbon–nutrient couplings in temperate forests
Richard P. Phillips et al., 2013. New Phytologist 199: 41–51 “Understanding the context dependence of ecosystem responses to global changes requires the development of new conceptual frameworks. Here we propose a framework for considering how tree species and their mycorrhizal associates differentially couple carbon (C) and nutrient cycles in temperate forests. Given that tree species predominantly associate with a single type of mycorrhizal fungi (arbuscular mycorrhizal (AM) fungi or ectomycorrhizal (ECM) fungi), and that the two types of fungi differ in their modes of nutrient acquisition, we hypothesize that the abundance of AM and ECM trees in a plot, stand, or region may provide an integrated index of biogeochemical transformations relevant to C cycling and nutrient retention.” Table S1 Species and mycorrhizal associations of all trees

Root morphology and mycorrhizal symbioses together shape nutrient foraging strategies of temperate trees
Weile Chen et al., 2016. PNAS 113 (31) 8741-8746 “Plant growth requires acquisition of soil nutrients in a patchy environment. Nutrient patches may be actively foraged by symbioses comprising roots and mycorrhizal fungi. Here, we show that thicker root tree species (e.g., tulip poplar, pine) respond weakly or not at all to nutrient heterogeneity. In contrast, thinner root tree species readily respond by selectively growing roots [arbuscular mycorrhizal trees (e.g., maple)] or mycorrhizal fungal hyphae [ectomycorrhizal trees (e.g., oak)] in nutrient-rich “hotspots.” Our results thus indicate predictable patterns of nutrient foraging among tree species with contrasting mycorrhiza types and root morphologies. These findings can pave the way for a more holistic understanding of root-microbial function, which is critical to plant growth and biogeochemical cycles in forested ecosystems.”

Evolution of trees and mycorrhizal fungi intensifies silicate mineral weathering
Joe Quirk et al., 2012. Biology Letters- Global change biology 8, 1006–1011

Mycorrhizal Networks & Forest Ecology & Management

The foundational role of mycorrhizal networks in self-organization of interior Douglas-fir forests by S. Simmard, 2009, Forest Ecology and Management 258S (2009) S95–S107

Architecture of the wood‐wide web: Rhizopogon spp. genets link multiple Douglas‐fir cohorts
Kevin J. Beiler et al., 2010 in new Phytologist 185: 543–553.

Ectomycorrhizae and forestry in British Columbia: A summary of current research and conservation strategies
Alan M. Wiensczyk et al., 2002 in B.C. Journal of Ecosystems and Management. Focus is on ectomycorrhiza. These benefits of ectomycorrhizal fungi for tree growth are cited (references excluded):

enhancing the uptake of essential nutrients (mainly
phosphorus and nitrogen) and water
protecting against pathogens  and heavy metals
binding soil particles to create favourable soil
facilitating below-ground nutrient transfer among
altering the competitive relationships among plants
of different species

These management practices are advised to maintain “these beneficial plant/
fungal associations across the landscape”:

Retaining refuge plants, mature trees, and oldgrowth forests;
Retaining the forest floor during harvest and mechanical site preparation;
Avoiding high-intensity broadcast burns;
Minimizing the effects of species shifts, particularly
following grass seeding;
Maintaining the edge-to-area ratio of harvested areas
within certain limits;
Planting a mixture of tree species soon after harvest;
Retaining coarse woody debris; and
Managing for the fruiting bodies formed by ectomycorrhizal fungi, including edible mushrooms and
truffles, fungi species used by wildlife, and rare and
endemic species.

Partial Retention of Legacy Trees Protect Mycorrhizal Inoculum Potential, Biodiversity, and Soil Resources While Promoting Natural Regeneration of Interior Douglas-Fir, Suzanne W Simard et al., 2021. From the Abstract:
Clearcutting reduces proximity to seed sources and mycorrhizal inoculum potential for regenerating seedlings. Partial retention of legacy trees and protection of refuge plants, as well as preservation of the forest floor, can maintain mycorrhizal networks that colonize germinants and improve nutrient supply. However, little is known of overstory retention levels that best protect mycorrhizal inoculum while also providing sufficient light and soil resources for seedling establishment. To quantify the effect of tree retention on seedling regeneration, refuge plant diversity, and resource availability, we compared five harvesting intensities with increasing retention of overstory trees (clearcutting (0% retention), seed tree (10% retention), 30% patch retention, 60% patch retention, and 100% retention in uncut controls) in an interior Douglas-fir-dominated forest in British Columbia… This study suggests that dispersed retention of overstory trees where seed trees are spaced ~10–20 m apart, and aggregated retention where openings are <60 m (2 tree-lengths) in width, will result in an optimal balance of seed source proximity, inoculum potential, and resource availability where seedling regeneration, plant biodiversity, and carbon stocks are protected.

Shifts in dominant tree mycorrhizal associations in response to anthropogenic impacts
Insu Jo et al., 2019 in Sci. Adv. 2019;5: eaav6358 10 April 2019 “We show that abundances of the two dominant mycorrhizal tree groups—arbuscular mycorrhizal (AM) and ectomycorrhizal trees—are associated primarily with climate. Further, we show that anthropogenic influences, primarily nitrogen (N) deposition and fire suppression, in concert with climate change, have increased AM tree dominance during the past three decades in the eastern United States. Given that most AM-dominated forests in this region are underlain by soils with high N availability, our results suggest that the increasing abundance of AM trees has the potential to induce nutrient acceleration, with critical consequences for forest productivity, ecosystem carbon and nutrient retention, and feedbacks to climate change.

Forest disturbances affect functional groups of macrofungi in young successional forests – harvests and fire lead to different fungal assemblages
J Kouki & Kauko Salo Forest Ecology and Management Volume 463, 1 May 2020, 118039 Highlights: Fungal groups responded in different ways to major disturbances in boreal forests. Fire promoted several pyrophilous species and distinct fungal assemblage. Clear-cut had a strong negative effect especially on ectomycorrhizal fungi (ECM). Living retention trees slightly alleviated negative effects of clear-cut on ECM. Early post-fire young forests can be highly valuable for fungal biodiversity.