Mathematical models describing the behavior of Komagataella phaffii in bioreactors are a powerful tool for process optimization and control. In this chapter, models accounting for different operation modes, namely batch, fed-batch, and continuous culture (i.e., chemostat) under different substrate regimes, have been considered through illustrative examples. Consideration has been given to the dynamics of both intracellular and extracellular components. Simulations highlighting specific variable behavior for each operation mode, such as biomass in fed-batch cultures and steady-state productivity in chemostats, have been included. In particular, the use of methanol with supplementary substrates, such as glycerol or sorbitol, and the integration of intracellular enzyme alcohol oxidase synthesis have been explored. The chapter provides a systematic protocol guiding readers to construct such kinetic models.