Stepping is a fundamental skill involved in common bipedal activities such as walking, foot repositioning and step recovery. Generating these stepping activities requires characters that are controllable and responsive. This dissertation describes a goal-directed controller and a momentum supervisor for characters that perform both believable and robust steps under a variety of conditions. The desired step is controlled by generic task goals, namely step position and step duration, which allow characters to step in arbitrary directions with various speeds. These high-level goals guide desired changes of a character's center of mass and swing foot over the duration of the step. To produce realistic and flexible steps, the desired time-varying values for the center of mass and the swing foot are derived from parametric curve generators which are built on empirical evidence extracted from motion capture data of stepping. Controlling these two values along with regulation of angular momentum in vertical axis produces characters with coordinated full-body movements including natural arm swings during stepping. The system can guide a character with purposeful, directable steps to precisely follow user-specified foot placements and to carefully control the character's position and orientation. Moreover, the same system can be used to create protective steps to maintain the character's balance in response to a perturbation. A novel supervisory routine automatically chooses when and where to step with a straightforward goal: removing all linear and angular momenta induced by a push. In contrast to previous methods for push recovery using the inverted pendulum, the proposed momentum supervisor introduces a nice clean formulation to determine when and where to step and provides better prediction of a character's stability under perturbations by considering both linear and angular momenta of the character. In addition to responding to a perturbation, this dissertation also presents an approach for characters that anticipate impending perturbations with examples taken from human motion capture data. I focus on the motion interpolation sysnthesis technique which allows a character to anticipate by blocking or dodging a threat coming from a variety of directions and targeting any part of the body.