The main advantage of superconductors, that these materials can transport electric current without energy dissipation, is achieved by the mechanism of flux pinning. Quantized flux lines that contain superconducting structure inside do not move under interaction with defects in the superconductor, even when the Lorentz force is present due to the current. As a consequence, no electromotive force appears, resulting in no energy dissipation. The mechanism of flux pinning is, in principle, reversible with respect to the motion of flux lines. The observed results are commonly irreversible, however, as described by the critical state model, which assumes that there is a balance between the Lorentz force and the irreversible pinning force. In this chapter, the summation theory is introduced, which is used to analytically determine the critical current density, i.e., the maximum non-dissipative current density. The reason why the resultant electromagnetic phenomena become irreversible is clarified, even though the fundamental flux pinning mechanism is reversible. The irreversibility in flux pinning phenomena does not originate from the breaking of time reversal symmetry, but is of another type, such as friction, that is non-dissipative in stationary condition, although it causes energy dissipation in motion due to the applied force. The upper limit of the critical current density that can be achieved by the flux pinning mechanism is discussed using the Ginzburg-Landau theory. Reference (Flux pinning in superconductors, 3rd edn. Springer, 2022 [1]) covers a wide area of the material in this chapter.