The early preimplantation mouse embryo is a unique system where it is possible to explore the foundations of totipotency and differentiation. Following fertilization, a single cell, the zygote, will give rise to all tissues of the organism. The first signs of differentiation in the embryo are evident at the blastocyst stage with the formation of the trophectoderm, a differentiated tissue that envelopes the inner cell mass. The question of when and how the cells start to be different from each other in the embryo is central to developmental biology: as cell fate decisions are undertaken, loss of totipotency comes about. Although the blastomeres of the preimplantation embryo are totipotent, as the embryo develops some differences appear to develop between them which are, at least partially, related to the epigenetic information of each of these cells. The hypothesis of epigenetic asymmetries acting as driver for lineage allocation is presented. Although there are now some indications that epigenetic mechanisms are involved in cell fate determination, much work is needed to discover how such mechanisms are set in play upon fertilization and how they are transmitted through cell division. These considerations are further discussed in the context of preimplantation genetic diagnosis: does it matter to the embryo which cell is used for genetic diagnosis? The exquisite complexity and richness of chromatin-regulated events in the early embryo will certainly be the subject of exciting research in the future.