  I review the application of self-consistent Green's functions methods to
study the properties of infinite nuclear systems. Improvements over the last
decade, including the consistent treatment of three-nucleon forces and the
development of extrapolation methods from finite to zero temperature, have
allowed for realistic predictions of the equation of state of infinite
symmetric, asymmetric and neutron matter based on chiral interactions.
Microscopic properties, like momentum distributions or spectral functions, are
also accessible. Using an indicative set of results based on a subset of chiral
interactions, I summarise here the first-principles description of infinite
nuclear system provided by Green's functions techniques, in the context of
several issues of relevance for nuclear theory including, but not limited to,
the role of short-range correlations in nuclear systems, nuclear phase
transitions and the isospin dependence of nuclear observables.
