In this work we analyze and review cosmological models in which the dynamics
of a single scalar field accounts for a unified description of the Dark Matter
and Dark Energy sectors, dubbed Unified Dark Matter (UDM) models. In this
framework, we consider the general Lagrangian of k-essence, which allows to
find solutions around which the scalar field describes the desired mixture of
Dark Matter and Dark Energy. We also discuss static and spherically symmetric
solutions of Einstein's equations for a scalar field with non-canonical kinetic
term, in connection with galactic halo rotation curves.Comment: 57 pages, 6 figures, LaTeX file. Typos corrected; Added References;
Revised according to reviewer's suggestions; Invited Review for the special
issue "Focus Issue on Dark Matter" for Advances in Astronom
