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The two main ingredients of what is currently the standard cosmological model, ΛCDM, are cold dark matter (CDM) and dark energy, vacuum (cosmological constant Λ) being its simplest form. In the first introductory part of the talk I will illustrate general aspects of this current cosmology, its problems and alternative lines of investigations. Assuming General Relativity (GR) as the theory of gravity, in the second part I will focus on recent work on one of many possible scenarios for dark energy: the interacting vacuum scenario. In essence this cosmology, from a methodological perspective, consists mostly of the application of linear relativistic perturbation theory of cosmological models. In the third part I will instead illustrate recent pioneering work on applying numerical relativity (fully nonlinear GR) to the nonlinear growth of structures in cosmology. This is a problem that has been traditionally studied using Newtonian N-body simulations. In the last few years it has emerged how nonlinear relativistic effects could be relevant for upcoming observational galaxy surveys, and how from these new insight can be gained both on the early universe and on new aspects of nonlinear structure formation in the late universe. In particular, I will illustrate how gravito-magnetism, a purely general-relativistic aspect of gravity, can be predicted from relativistic simulations. I will conclude by illustrating future directions of research.
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