This paper introduces the concept of gait transitions, acyclic feedforward motion patterns that allow a robot to switch from one gait to another. Legged robots often utilize collections of gait patterns to locomote over a variety of surfaces. Each feedforward gait is generally tuned for a specific surface and set of operating conditions. To enable locomotion across a changing surface, a robot must be able to stably change between gaits while continuing to locomote. By understanding the fundamentals of gaits, we present methods to correctly transition between differing gaits. On two separate robotic platforms, we show how the application of gait transitions enhances each robot's behavioral suite. Using the RHex robotic hexapod, gait transitions are used to smoothly switch from a tripod walking gait to a metachronal wave gait used to climb stairs. We also introduce the RiSE platform, a hexapod robot capable of vertical climbing, and discuss how gait transitions play an important role in achieving vertical mobility