In the 1980s, Escherichia coli was the preferred host for heterologous protein expression owing to its capacity for rapid growth in complex media; well-studied genetics; rapid and direct transformation with foreign DNA; and easily scalable fermentation. Despite the relative ease of use of E. coli for achieving the high expression of many recombinant proteins, for some proteins, e.g., membrane proteins or proteins of eukaryotic origin, this approach can be rather ineffective. Another microorganism long-used and popular as an expression system is baker’s yeast, Saccharomyces cerevisiae. In spite of a number of obvious advantages of these yeasts as host cells, there are some limitations on their use as expression systems, for example, inefficient secretion, misfolding, hyperglycosylation, and aberrant proteolytic processing of proteins. Over the past decade, nontraditional yeast species have been adapted to the role of alternative hosts for the production of recombinant proteins, e.g., Komagataella phaffii, Yarrowia lipolytica, and Schizosaccharomyces pombe. These yeast species’ several physiological characteristics (that are different from those of S. cerevisiae), such as faster growth on cheap carbon sources and higher secretion capacity, make them practical alternative hosts for biotechnological purposes. Currently, the K. phaffii-based expression system is one of the most popular for the production of heterologous proteins. Along with the low secretion of endogenous proteins, K. phaffii efficiently produces and secretes heterologous proteins in high yields, thereby reducing the cost of purifying the latter. This review will discuss practical approaches and technological solutions for the efficient expression of recombinant proteins in K. phaffii, mainly based on the example of enzymes used for the feed industry.