Harmonic map theory for singular targets was first introduced in the early 90's by Gromov and Schoen to prove p-adic superrigidity, and later generalized further in different directions by different authors.  We will first describe several notions of energy of maps and harmonic maps into singular spaces.  We will discuss the roles of domain and target curvatures in the geometry of harmonic maps, and recover a Bochner formula and a number of Liouville theorems along the way.