Spiking neural (SN) P systems are a class of distributed parallel computing devices inspired by the way neurons communicate by means of spikes. In this work, we investigate reversibility in SN P systems, as well as the computing power of reversible SN P systems. Reversible SN P systems are proved to have Turing creativity, that is, they can compute any recursively enumerable set of non-negative integers by simulating universal reversible register machine.