This paper seeks to review the developments in the field within the framework of stability and control of systems subject to unilateral constraints. Particular emphasis is given to three main issues that, in our view, form the underlying theory in the study of such systems. Impact of the lower limbs with the walking surface and its effect on the walking dynamics is considered first. Several key issues such as multiple impacts, restitution and friction laws, and existence and uniqueness of solutions are reviewed in detail. Next, we consider the dynamic stability of bipedal gait. We review the use of discrete maps in studying the stability of the closed orbits that represent the dynamics of a biped, which can be characterized as a hybrid system. Last, we consider the control schemes that have been used in regulating the motion of bipedal systems, and we seek to identify the needed future developments. This paper seeks to review the developments in the field within the framework of stability and control of systems subject to unilateral constraints. Particular emphasis is given to three main issues that, in our view, form the underlying theory in the study of such systems. Impact of the lower limbs with the walking surface and its effect on the walking dynamics is considered first. Several key issues such as multiple impacts, restitution and friction laws, and existence and uniqueness of solutions are reviewed in detail. Next, we consider the dynamic stability of bipedal gait. We review the use of discrete maps in studying the stability of the closed orbits that represent the dynamics of a biped, which can be characterized as a hybrid system. Last, we consider the control schemes that have been used in regulating the motion of bipedal systems, and we seek to identify the needed future developments.