Laplace operators have been studied extensively on polyhedral surfaces and remain to be one of the central building blocks for geometry processing applications. In this talk we will focus on the Bilaplacian, which poses additional challenges when it comes to convergence analysis. In particular, we will consider a popular discretization of the Bilaplacian on polyhedral surfaces ? the mixed finite element cotangent discretization ? and investigate its convergence under mesh refinement. Our convergence result generalizes the case of planar domains that was investigated by Scholz in 1978. We are also going to look at some applications of the Bilaplacian in geometry processing, such as interpolation, smoothing, character animation, and more. This is joint work with Oded Stein, Eitan Grinspun, and Alec Jacobson.