The methylotrophic yeast Pichia pastoris (Komagataella phaffii) is currently considered one of the most promising hosts for recombinant protein production (RPP) and metabolites due to the availability of several tools to efficiently regulate the recombinant expression, its ability to perform eukaryotic post-translational modifications and to secrete the product in the extracellular media. The challenge of improving the bioprocess efficiency can be faced from two main approaches: the strain engineering, which includes enhancements in the recombinant expression regulation as well as overcoming potential cell capacity bottlenecks; and the bioprocess engineering, focused on the development of rational-based efficient operational strategies. Understanding the effect of strain and operational improvements in bioprocess efficiency requires to attain a robust knowledge about the metabolic and physiological changes triggered into the cells. For this purpose, a number of studies have revealed chemostat cultures to provide a robust tool for accurate, reliable, and reproducible bioprocess characterization. It should involve the determination of key specific rates, productivities, and yields for different C and N sources, as well as optimizing media formulation and operating conditions. Furthermore, studies along the different levels of systems biology are usually performed also in chemostat cultures. Transcriptomic, proteomic and metabolic flux analysis, using different techniques like differential target gene expression, protein description and 13C-based metabolic flux analysis, are widely described as valued examples in the literature. In this scenario, the main advantage of a continuous operation relies on the quality of the homogeneous samples obtained under steady-state conditions, where both the metabolic and physiological status of the cells remain unaltered in an all-encompassing picture of the cell environment. This contribution aims to provide the state of the art of the different approaches that allow the design of rational strain and bioprocess engineering improvements in Pichia pastoris toward optimizing bioprocesses based on the results obtained in chemostat cultures. Interestingly, continuous cultivation is also currently emerging as an alternative operational mode in industrial biotechnology for implementing continuous process operations.