  The Density Matrix Renormalization Group (DMRG) has become a powerful
numerical method that can be applied to low-dimensional strongly correlated
fermionic and bosonic systems. It allows for a very precise calculation of
static, dynamic and thermodynamic properties. Its field of applicability has
now extended beyond Condensed Matter, and is successfully used in Statistical
Mechanics and High Energy Physics as well. In this article, we briefly review
the main aspects of the method. We also comment on some of the most relevant
applications so as to give an overview on the scope and possibilities of DMRG
and mention the most important extensions of the method such as the calculation
of dynamical properties, the application to classical systems, inclusion of
temperature, phonons and disorder and a recent modification for the {\it ab
initio} calculation of electronic states in molecules.
