In Europe and America, "mushrooms" in a recipe usually refers to button mushrooms (Agaricus bisporus), which were first cultivated in France in the 1600's. In Far East Asia, the equivalent is Shiitake, which has long been the cultivated "food mushroom" of choice. Only in the past few decades has Shiitake become a household name in western cuisine.
Originating in China, wild Shiitake is also commonly known as Black Mushroom and Chinese Mushroom. The name Shiitake comes from the Chinese Shii Tree, which is the most common host tree. But it can also grow on beeches and oaks. The cultivation of Shiitake in China and Japan goes back at least 1000 years.
What is less known in the West is that in the form of Shiitake extract, this is also the most studied medicinal mushroom of the Orient. The primary focus of research has been on the anti-viral  and anti-tumoral  properties.
The preferred part of Shiitake to use medicinally is the mycelium (the "roots") because they contain compounds that either don't exist in the fruit body ("mushroom"), or are much more concentrated in the mycelium.
The most common extract is known as LEM, a protein extract from Lentinula Edodes Mycelia. (Lentinula edodes is Latin for Shiitake.) LEM has been shown to have powerful immune boosting properties, [95, 96, 97] particularly anti-bacterial. [98, 99] LEM has also been found to exhibit anti-cancer properties.  One study found it to kill melanoma cells while causing no harm to healthy cells. 
Lentinan is the name of another much researched compound isolated from Shiitake, named after the Latin genus name Lentinula. Lentinan is a polysaccharide that has been found to stimulate the human immune system to combat cancer. [102, 103, 104, 105, 106, 107, 108, 109, 110] It is currently used in Asia as an intravenous cancer drug.
Arabinoxylanes, compounds resulting from Shiitake-on-rice fermentation, have also demonstrated significant anti-viral activity. [111, 112, 113]
Two viruses in particular that have been studied with promising results are herpes simplex type 1  and HIV [115, 116, 117]. It should be mentioned, however, that the previously mentioned Lentinan as an isolated compound does not appear to affect HIV replication. 
Other studies worth a brief mention have reported positive findings in the use of Shiitake extract to prevent septic shock,  and to treat Candida  and chronic fatigue syndrome. 
And last but not least, in his book Mycelium Running, foremost U.S. medicinal mushroom expert Paul Stamets also lists the following areas where Shiitake has been reported as having a therapeutic effect: Blood sugar; blood pressure; kidney support; cholesterol; liver health; stress; sexual dysfunction; breast cancer; prostate cancer; liver cancer. 
Note: The statements on this page have not been evaluated by the Food and Drug Administration. This article is not intended to diagnose, treat, cure or prevent any disease. Never use any herb (or mushroom) except as advised by a licensed medical practitioner.
Credit to Paul Stamets for research and source material.