In recent years, there has been an increasing demand for new sources of protein, both for human and animal nutrition. In addition to alternative sources of protein, such as algae or edible insects, protein obtained from yeast and mold biomass is becoming more and more important. The main fungal protein producers are the yeasts Saccharomyces cerevisiae, Kluyveromyces marxianus, Candida utilis, Yarrowia lipolytica, and the molds Fusarium venenatum, Aspergillus oryzae, and Monascus purpureus. The production of fungal protein has many advantages, including the ability to regulate the amino acid composition, high protein content in dry matter, the possibility of production in a continuous process, independence from climatic factors, and the possibility of using waste substrates as ingredients of media. One of the disadvantages is the high content of nucleic acids, which generates the need for additional purification procedures before use in food. However, a number of enzymatic, chemical, and physical methods have been developed to reduce the content of these compounds. The paper presents the current state of knowledge about fungal producers, production and purification methods, the global market, as well as opportunities and challenges for single-cell protein (SCP) production.