In this talk, I will give an introduction to subdivision schemes, which are iterative refinement processes for interpolating or approximating discrete data points. Most result on subdivision schemes concern data in vector spaces and rules which are linear. I will present an adaptation of subdivision schemes to operate on manifold-valued data using the intrinsic geometry of the underlying manifold (such as the exponential map). Analysis of convergence and smoothness properties will be presented as well. Subdivision schemes find applications in computer graphics and 3D animated movies.