The main purpose of this reprint is to present different approaches most commonly employed in the analysis of bioprocesses. This reprint aims to develop, in some detail, the bases and concepts of bioprocesses related to the bioprocess analysis introduced in basic principles of mathematical modeling. From this viewpoint, the system's approach to bioengineering and bioprocessing, with its current focus on the development of mathematical approaches and their analysis, is a logical sequel in understanding the mechanisms of cellular and metabolic processes. Specifically, it concerns applications in modeling, estimation, and optimization of bioprocesses. Consequently, this reprint presents key results in various fields, including dynamic modeling, dynamic properties of bioprocess models, online estimation of parameters and state variables, and optimization of bioprocesses.