The journey of embryonic development starts at oocyte fertilization, which triggers a complex cascade of events and cellular pathways that guide early embryogenesis. Recent technological advances have greatly expanded our knowledge of cleavage-stage embryo development, which is characterized by an increased rate of whole-chromosome losses and gains, mixoploidy, and atypical cleavage morphokinetics. Embryonic aneuploidy significantly contributes to implantation failure, spontaneous miscarriage, stillbirth or congenital birth defects in both natural and assisted human reproduction. Essentially, early embryo development is strongly determined by maternal factors. Owing to considerable limitations associated with human oocyte and embryo research, the use of animal models is inevitable. However, cellular and molecular mechanisms driving the error-prone early stages of development are still poorly described. In this review, we describe known events that lead to aneuploidy in mammalian oocytes and preimplantation embryos. As the processes of oocyte and embryo development are rigorously regulated by multiple signal-transduction pathways, we explore the putative role of signaling pathways in genomic integrity maintenance. Based on the existing evidence from human and animal data, we investigate whether critical early developmental pathways, like Wnt, Hippo and MAPK, together with distinct DNA damage response and DNA repair pathways can be associated with embryo genomic instability, a question that has, so far, remained largely unexplored.