We first give a general introduction to harmonic maps, especially from (universal cover of) a Riemann surface into hyperbolic surfaces, symmetric spaces, and singular spaces. We then explain why they are useful to study moduli space of surface group representations into PSL(2,R) and general Lie groups, and to study compactification of these moduli spaces. This talk will be introductory and expository. We emphasize on PSL(2,R) case to give a guiding picture and then explain other examples.