The purpose of this work is to present a set of mathematical tools that can simplify studying robotic walking motions and designing energy-efficient controllers. The authors extend classical dynamic modeling methods and view robots and controllers as energy-exchanging physical systems, which forms the basisof the so-called port-based approach. They show how such methods can be used to analyze walking mechanisms, find efficient walking trajectories, and design controllers that increase robustness and stability with minimal energy cost. Extensive examples and illustrations are used with the objective to make the mathematics intuitive and accessible to everyone with an engineering background.