Coating a rigid surface with a thin layer of a stimulus-responsive polymer gel provides a convenient means to create surfaces with responsive properties such as biocompatibility, adhesion, and tribology. However, as the gel increases its level of swelling, the constraint imposed by the substrate can result in large in-plane compressive stresses, in some cases leading to a creasing instability of the gel surface. While this instability has been known in practice for well over a century, it remains poorly understood. Using model polyacrylamide and poly(N-isopropyl acrylamide) copolymer gels, we have studied the onset of creasing as a function of material properties and gel thickness, and addressed basic questions regarding crease morphologies and growth mechanisms. Using the understanding gained from these studies, we are developing this instability as a route to create active surfaces, where we can exercise control over surface topography and chemical patterns in both space and time.