In this talk I first discuss our recent use of perturbatively selected configuration interaction expansions for building accurate trial wavefunctions for diffusion Monte Carlo (DMC) calculations. I argue that by using such expansions an improved control of the fixed-node error is possible. Second, I present a newly introduced stochastic approach to compute very efficiently the second-order energy correction of multireference perturbation theories (MRPT2, CASPT2, NEVPT2,...).