This paper gives a comprehensive introduction to logical control systems (LCSs), including its history, the logical background, the expression, the fundamental mathematical tool, and the analyzing method. Particularly, it is emphasized on the major achievements on logical dynamic systems (LDSs) and their control theory in last few years, consisting of (i) the topological structure of LDSs; (ii) controllability, observability, stability and stabilization, disturbance decoupling, optimal control, identification of logical (control) systems; (iii) the extension of the results about Boolean systems to k-valued and mix-valued logical (control) systems. These results form the foundation of logical control system theory (LCST). In addition, the concepts, notations, and the fundamental method/tool have been formally normalized. Some current developments of LCST and its applications or potential applications are discussed in detail. Some open problems and possible research directions are introduced.