The limited kinematic hardening plasticity theory is re-examined and presented with additional clarifying hypotheses being proposed. The general theory forms the base for construction of the path-independent shakedown theorems intended for possible broad engineering applications, and possible further specifications of particular hardening laws. Some specifications in the literature on limited kinematic hardening are critically analysed. Recent applications of the shakedown theorems in path-independent forms with two separated modes, which are only fully founded in this study, and further problems are briefly summarized with references to the respective literature.