New species of fungi that belong to the class Wallemiomycetes and related lineages were discovered and characterized. The Wallemiomycetes includes species of brown moulds from the genus Wallemia. Further study was warranted for Wallemia sebi because of its ubiquity in the human indoor environments and its potential roles in food spoilage, human allergy and disease. A survey of Wallemia in house dust was conducted. Sequencing of DNA and application of the genealogical concordance phylogenetic species recognition (GCPSR) led to recognition of four species within the W. sebi species complex (WSSC) and served as the foundation for phenotypic assessment and the formal description of three new species called W. mellicola, W. canadensis and W. tropicalis. A survey of heat resistant fungi in soils coincidentally resulted in the discovery of a new lineage of fungi related to Wallemia. This new lineage included a previously described monotypic genus Basidioascus and a new sister genus given the name Geminibasidium. A part of the morphological life cycle of these fungi was documented where two new basidial types were discovered, followed by the description of three new species called B. magus, G. donsium and G. hirsutum. Further studies on the sexuality and origins of the species B. undulatus were carried out with genome sequencing, genome analysis, confocal microscopy and electron microscopy. These results led to the creation of a new class of fungi called the Geminibasidiomycetes, which are distantly related to the Wallemiomycetes. Solving the WSSC, circumscribing a new class of fungi called Geminibasidiomycetes and characterizing the species of Geminibasidiomycetes on a taxonomic and genomic level are my original contributions to scientific knowledge.