In this review, we present our recent evidence suggesting, but not yet proving, that mammalian spermatozoa contain a mechanism by which they can digest their own DNA when exposed to a stressful environment. We discuss our recent data that demonstrate that when mammalian spermatozoa are treated in a variety of ways, the paternal chromosomes in the zygote, or the sperm DNA itself, are degraded into large, chromosome-sized fragments. These published data support the existence of nuclease activity in spermatozoa. We suggest that this nuclease activity is part of a mechanism the spermatozoon uses when it encounters a stressful environment to prevent fertilisation and to avoid the transmission of potentially damaged DNA to the embryo. We propose a model based on sperm chromatin structure by which this nuclease can digest the highly condensed sperm chromatin.