The paper presents the main features of the Non-Smooth Contact Dynamics (NSCD) method, which is used to solve dynamical frictional contact problems for systems with numerous contacting points, particularly large collections of rigid or deformable bodies. The method models unilateral contact using the Signorini condition and Coulomb's law, and employs fully implicit algorithms to handle the complexity of such systems. The author emphasizes the importance of contact between deformable bodies and provides numerical simulation examples for granular materials, deep drawing, and buildings made of stone blocks. The paper also discusses the discretization of continuous media, the discrete form of the dynamical equation, and the solution of the basic frictional contact problem. It introduces the quasi-inelastic shock law for handling inelastic shocks and provides numerical schemes for the dynamical equation, including the theta method and the implicit Euler method. The NSCD method is shown to behave well when the time step is small and the friction coefficient is within the allowed range, and it has been proven mathematically for the dynamical frictional problem of a discrete system of particles with elastoplastic internal forces.The paper presents the main features of the Non-Smooth Contact Dynamics (NSCD) method, which is used to solve dynamical frictional contact problems for systems with numerous contacting points, particularly large collections of rigid or deformable bodies. The method models unilateral contact using the Signorini condition and Coulomb's law, and employs fully implicit algorithms to handle the complexity of such systems. The author emphasizes the importance of contact between deformable bodies and provides numerical simulation examples for granular materials, deep drawing, and buildings made of stone blocks. The paper also discusses the discretization of continuous media, the discrete form of the dynamical equation, and the solution of the basic frictional contact problem. It introduces the quasi-inelastic shock law for handling inelastic shocks and provides numerical schemes for the dynamical equation, including the theta method and the implicit Euler method. The NSCD method is shown to behave well when the time step is small and the friction coefficient is within the allowed range, and it has been proven mathematically for the dynamical frictional problem of a discrete system of particles with elastoplastic internal forces.