Session-based communication has gained a widespread acceptance in practice as a means for developing safe communicating systems via structured interactions. In this paper, we investigate how these structured interactions are affected by reversibility, which provides a computational model allowing executed interactions to be undone. In particular, we provide a systematic study of the integration of different notions of reversibility in both binary and multiparty single sessions. The considered forms of reversibility are: one for completely reversing a given session with one backward step, and another for also restoring any intermediate state of the session with either one backward step or multiple ones. We analyse the costs of reversing a session in all these different settings. Our results show that extending binary single sessions to multiparty ones does not affect the reversibility machinery and its costs.