The extension of ab initio Monte Carlo methods to the study of excited states is a challenging problem at the forefront of present research in the field of computational techniques applied to the quantum many-body problem. The aim is to calculate excited states with similar accuracy to the one achieved in the study of the ground-state properties. We present an state of the art of such applications devoting special attention to the formalism behind the algorithms recently used: fixed node diffusion Monte Carlo (FN-DMC), fixed phase diffusion Monte Carlo (FP-DMC), and released node diffusion Monte Carlo (RN-DMC). As examples of these calculations, we present results on the structure of a vortex excitation and the well known phonon-roton branch in superfluid 4-He at zero temperature. The difficult problem of the continuation of imaginary-time quantum Monte Carlo data is also discussed. The most commonly method used, i.e. bayesian inference, is presented together with some results on the dynamical structure factor in liquid 4-He.