Recent developments in quantum Monte Carlo simulations with applications for cold gases

This is a review of recent developments in Monte Carlo methods in the field of ultracold gases. For bosonic atoms in an optical lattice we discuss path-integral Monte Carlo simulations with worm updates and show the excellent agreement with cold atom experiments. We also review recent progress in simulating bosonic systems with long-range interactions, disordered bosons, mixtures of bosons and spinful bosonic systems. For repulsive fermionic systems, determinantal methods at half filling are sign free, but in general no sign-free method exists. We review the developments in diagrammatic Monte Carlo for the Fermi polaron problem and the Hubbard model, and show the connection with dynamical mean-field theory. We end the review with diffusion Monte Carlo for the Stoner problem in cold gases.