  Quantum Monte Carlo methods are first-principle approaches that approximately
solve the Schr\"odinger equation stochastically. As compared to traditional
quantum chemistry methods, they offer important advantages such as the ability
to handle a large variety of many-body wave functions, the favorable scaling
with the number of particles, and the intrinsic parallelism of the algorithms
which are particularly suitable to modern massively parallel computers. In this
chapter, we focus on the two quantum Monte Carlo approaches most widely used
for electronic structure problems, namely, the variational and diffusion Monte
Carlo methods. We give particular attention to the recent progress in the
techniques for the optimization of the wave function, a challenging and
important step to achieve accurate results in both the ground and the excited
state. We conclude with an overview of the current status of excited-state
calculations for molecular systems, demonstrating the potential of quantum
Monte Carlo methods in this field of applications.
