  We review some general aspects of Horava-Lifshitz cosmology. Formulating it
in its basic version, we extract the cosmological equations and we use
observational data in order to constrain the parameters of the theory. Through
a phase-space analysis we extract the late-time stable solutions, and we show
that eternal expansion, and bouncing and cyclic behavior can arise naturally.
Concerning the effective dark energy sector we show that it can describe the
phantom phase without the use of a phantom field. However, performing a
detailed perturbation analysis, we see that Horava-Lifshitz gravity in its
basic version suffers from instabilities. Therefore, suitable generalizations
are required in order for this novel theory to be a candidate for the
description of nature.
