Fungi are a vital component of soil life constituting 70% of the biomass in healthy soils. Within a gram of healthy soil, there are between 10 and 20 million fungi and between 3 and 300 metres of fungal hyphae (roots)!
There are three categories of fungi: saprophytes, mutualists and pathogens.
Pathogens, as the name suggests, are the harmful fungi that do damage to plants and are the source of many plant diseases.
Saprophytes (often called saprotrophs today), are decomposers. Though they make up less than 1% of soil fungi, they are important in recycling carbon, nitrogen, phosporus and potassium. When you pile on the sheet mulch or do chop-and-drop mulching, saprophytes go to work breaking down that material and turning it into soil.
Mutualists are a plant's best friend. What is really important for us in permaculture are connections. Mutualists are often referred to as mycorrrhizae, but that term really refers to the symbiotic fungi-plant connections. The fungal hyphae connect not only fungus to one plant but multiple plants. Furthermore, these mycorrhizae are the conduit for photosynthate (sugars and other carbohydrates that are the product of photosynthesis) and nutrients between plants of different species. And some fungi can even help some tree better survive acid rain by assisting in the uptake of calcium. It's not a dog-eat-dog world, it's a friendly neighbour world!
Additionally, fungal hyphae also encourage beneficial bacteria, and together, they make up the vital crumb-like structure of healthy soil. Such soils are more easily penetrated by air, water and plant roots. Additionally, because soil with a crumb structure holds water better, it is more drought proof (meaning less irrigation is needed) and less prone to waterlogging.
Among the mycorrhizae are endomycorrhizae, which enters right into the cell wall of plants' roots to exchange nutrients, and ectomycorrhizae, which pass between root cells but do not enter the cell wall. Ectomycorrrhizae are also the kind that sometimes form truffles of mushrooms. One of the limiting factors to plant growth is the uptake of phosphorous. This is where mutualist mycorrhizae become vital. They scoop up the phosphorous in the soil and supply it to plants. The plants in turn supply the fungi with sugars.
Not every plant responds to mutualist fungi, however. Among plants that don't are members of the amaranthaceae (think amaranth and Chinese spinach) including its subfamily chenopodiaceae (think beets and chards), many brassicaceae (the mustard family which includes broccoli, cauliflower, cabbage, kale, brussels sprouts, turnip and others), the aizoaceae family (iceplant) and the cyperaceae family (bulrushes, sedge, papyrus, etc.). Knowing this, one might see a pattern of degraded lands with poor mycorrhizae having many of these plants in them. Such lands can be repaired by deep mulching and innoculating the soils with samples of healthy soils.
Also, soils that are high in sodium, chlorine, boron, cadmium, zinc or manganese can be detrimental to fungi. Highly acidic soils damaged by acid rain may lead to the formation of aluminum sulfate or aluminum nitrate which is toxic not only to plants but to fungi as well.
To promote fungal life which leads to healthy soils plant cover crops that will provide a permanent host for mycorrhizal fungi, avoid disturbing the land (ie. no-till agriculture), avoid the use of artificial fertilisers (many of which contain toxic cadmium!) and do not use herbicides or pesticides.