Chemical processes often exhibit nonlinear dynamics and tend to generate complex state trajectories, which present challenging operational problems due to complexities such as output multiplicity, oscillation, and even chaos. For this reason, a complete knowledge of the static and dynamic nature of these behaviors is required to understand, to operate, to control, and to optimize continuous stirred tank reactors (CSTRs). Through nonlinear analysis, the possibility of output multiplicity, self-sustained oscillation, and torus dynamics are studied in this paper. Specifically, output multiplicity is investigated in a case-by-case basis, and related operation and control strategies are discussed. Bifurcation analysis to identify different dynamic behaviors of a CSTR is also implemented, where operational parameters are identified to obtain self-oscillatory dynamics and possible unsteady-state operation strategy through designing the CSTR as self-sustained periodic. Finally, a discussion on codimension-1 bifurcations of limits cycles is also provided for the exploration of periodic forcing on self-oscillators. Through this synergistic study on the CSTRs, possible output multiplicity, oscillatory, and chaotic dynamics facilitates the implementation of novel operation/control strategies for the process industry.