Medical imaging problems, such as CT or MR imaging can be framed as Bayesian inverse imaging problems. The treatment of such problems frequently requires us to draw samples from high dimensional Gibbs distributions of the form p(x) = exp(-U(x))/Z with some potential function U(x). Sampling from such distributions is often done using discretizations of the Langevin stochastic differential equation. Unfortunately, however, in high dimensions and/or for complex distributions, these methods are computationally very expensive. In this talk we will discuss different strategies to accelerate sampling, involving momentum-based acceleration, successive approximation techniques such as annealed Langevin sampling, and acceleration by preconditioning. We will provide theoretical as well as numerical results for the different strategies on small scale and medical imaging examples.