What is the largest living fungus on Earth by area?

The largest living fungus known by area is Armillaria ostoyae. In Oregon’s Malheur National Forest, a genetically identified fungal colony of this species covers roughly 3.5 square miles, or about 9 square kilometres.

The visible honey mushrooms are only the reproductive fruiting bodies. Most of the organism consists of an underground network of mycelium and dark, cord-like rhizomorphs that spread beneath bark, through soil, and between tree roots. Genetic analysis is what allows researchers to determine that widely separated growth is part of one clonal individual rather than many unrelated mushrooms.

The Oregon colony is estimated to be thousands of years old and may weigh tens of thousands of tons, although the exact age and mass are estimates. Armillaria ostoyae is also a serious forest pathogen: it attacks roots and causes Armillaria root disease in conifers. This answer refers to the largest fungal colony by area, not the largest individual mushroom cap or fruiting body.