Lion's mane mushrooms, or Hericium erinaceus, is an edible mushroom that can be cultivated. In the wild these can get very large. It is native to North America and I have seen these pretty often in Oregon. This was grown on a sawdust recipe in a controlled environment in our growth chambers. This fungus is also called bearded tooth, pompom, satyr's beard and bearded hedgehog.
Button mushrooms, or Agaricus bisporus, are a well-known cultivated fungus. The white cap of the button mushroom is a mutation that has been adopted by the mushroom growing industry as these are also grown with a brown cap. These mushrooms are also referred to as portobello when it is older and more mature. It is also known as the cremini. A common mushroom pathogen is Pseudomonas tolaasii which causes brown blotch. Below is a photo showing the typical lesion symptoms of brown blotch. These were grown in a box lined with plastic and filled with a synthetic compost with a peat moss casing.
Lentinula edodes, or the shiitake mushroom, is native to East Asia. It is grown widely in both China and Japan. These mushrooms grow on shaded hardwood logs near a water source in the wild. In the United States, shiitake was not cultivated until the early 1970s as USDA put a quarantine on a closely related fungus that was known to attack railroad ties. Currently this mushroom is also widely cultivated within the U.S.A. These pictured were grown on a sawdust recipe with millet and bran. The hyphae was allowed to brown in the bag where the tops were cut off after pigmentation occurred. This is opposed to browning outside of the bag which removes the top and lowers humidity and after browning occurs, refrigerating followed by soaking. Both of these methods affect yields and break (or flush) frequencies.