The chapter describes stochastic models of shapes from a Hamiltonian viewpoint, including Langevin models, Riemannian Brownian motions and stochastic variational systems. Starting from the deterministic setting of outer metrics on shape spaces and transformation groups, we discuss recent approaches to introducing noise in shape analysis from a physical or Hamiltonian point of view. We furthermore outline important applications and statistical uses of stochastic shape models, and we discuss perspectives and current research efforts in stochastic shape analysis.