The neural control of balance during locomotion is currently not well understood, even in the light of considerable advances in research on balance during standing. In this paper, we lay out the control problem for this task and present a list of different strategies available to the central nervous system to solve this problem. We discuss the biomechanics of the walking body, using a simplified model that iteratively gains degrees of freedom and complexity. Each addition allows for different control strategies, which we introduce in turn: foot placement shift, ankle strategy, hip strategy, and push-off modulation. The dynamics of the biomechanical system are discussed using the phase space representation, which allows illustrating the mechanical effect of the different control mechanisms. This also enables us to demonstrate the effects of common general stability strategies, such as increasing step width and cadence.