The purpose of this contribution is to present the different classes of solutions that exist for self-similar spherically symmetric spacetimes with a perfect fluid as matter source. In particular, there is a class of ‘asymptotically Minkowski’ solutions that was discovered only recently. This class of solutions appears to be of relevance in the study of critical phenomena in spherically symmetric perfect-fluid collapse. The results presented here are part of an investigation [1,2], in which the work of Carr & Coley [3] has been combined with that of Goliath, Nilsson & Uggla [4,5]. ©1999 American Institute of Physics.