In this paper we advance the state of the art on the subject of bisimulations for logics of strategies. Bisimulations are a key notion to study the expressive power of a modal language, as well as for applications to system verification. In this contribution we present novel notions of bisimulation for several significant fragments of Strategy Logic (SL), and prove that they preserve the interpretation of formulas in the corresponding fragments. In selected cases we are able to prove that such bisimulations enjoy the Hennessy-Milner property. Finally, we make use of bisimulations to study the expressiveness of the various fragment of SL, including the complexity of their model checking problems.