  Harmonic maps are nonlinear extensions of harmonic functions. They are
critical points of natural energy functionals between Riemannian manifolds.
Such type of problems appear in Physics, Geometry of Finance and the study of
regularity and singularity uses methods from elliptic PDE, calculus of
variations and geometric measure theory. In this paper, we present a general
review of harmonic maps. It is a survey that aims to cover the main classical
known results regarding the harmonic maps. We present results for the
regularity, blow-ups and rectifiability for local minimizers, stationary
harmonic maps and weakly harmonic maps.
