  The problem of accurately determining the equation of state of nuclear and
neutron matter at density near and beyond saturation is still an open
challenge. In this paper we will review the most recent progress made by means
of Quantum Monte Carlo calculations, which are at present the only ab-inito
method capable to treat a sufficiently large number of particles to give
meaningful estimates depending only on the choice of the nucleon-nucleon
interaction. In particular, we will discuss the introduction of
density-dependent interactions, the study of the temperature dependence of the
equation of state, and the possibility of accurately studying the effect of the
onset of hyperons by developing an accurate hyperon-nucleon and
hyperon-nucleon-nucleon interaction.
