We present and discuss the properties of host galaxies of short Gamma-ray Burst (SGRBs). In particular, we examine those observations that contribute to the understanding of the progenitor systems of these explosions. Most SGRB hosts are found to be star forming objects, but an important fraction, similar to 1/5, of all hosts are elliptical with negligible star formation. Short bursts often occur at very large off-sets from their hosts, in regions where there is little or no underlying host light. Such results have enabled the community to test and improve the models for the production of short GRBs. In particular, the data are in favour of the merger of compact object binaries, provided that the kick velocities from the birth site are a few tens of km/s, and merger times of similar to 1 Gyr.