Locomotion of multibody systems in resistive media can be based on periodic change of the system configuration. The following types of mobile robotic systems are examined in the paper: multilink snake-like systems; multibody systems in quasi-static motion; systems consisting of several interacting bodies; fish-like, frog-like, and boat-like systems swimming in fluids; systems containing moving internal masses. Dynamics of these systems subjected to various resistance forces, both isotropic and anisotropic, are investigated, including dry friction forces obeying Coulomb\mbox{'}s law and forces directed against the velocity of the moving body and proportional to the velocity value or its square. Possible modes of locomotion and control algorithms are discussed. Optimization for various types of mobile robots is considered. Optimal values of geometrical and mechanical parameters as well as optimal controls are obtained that provide the maximum locomotion speed or minimum energy consumption. Results of experiments and computer simulation are discussed.