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This article describes how to use level sets to represent and compute deformable surfaces. A deformable surface is a sequence of surface models obtained by taking an initial model and incrementally modifying its shape. Typically, we can parameterize the deformation over time, and thus we can imagine that a surface moves or flows under the influence of a vector field. The surface flow, v, can be determined as a function of spatial position (and time), or it can depend on the shape of the surface itself. The latter is called a geometric flow. Deformable surfaces have been used to solve a variety of problems in image processing, computer vision, visualization, and graphics. In graphics, for instance, deformable surface models have been used to form sequences of shapes that animate the morphing of one object into another. They have also been used to denoise or smooth surface models derived from a set of noisy 3D measurements.