Chromosome segregation in female germ cells and early embryonic blastomeres is known to be highly prone to errors. The resulting aneuploidy is therefore the most frequent reason for termination of early development and embryo loss in mammals. And when compatible with embryonic and foetal development, aneuploidy leads into severe developmental disorders. The main surveillance mechanism, essential for protection of cells against aneuploidy, is the Spindle Assembly Checkpoint (SAC). And although all eukaryotic cells are perhaps able to mount SAC response, it is not clear, whether this pathway is active in all cell types, including blastomeres of early embryos. In this review, we will summarize and discuss the published literature with regards to mechanisms controlling chromosome segregation in early embryos. Our conclusion is that early embryos show limited capabilities to react to chromosome segregation defects, which might, at least partially, explain the widespread problem of aneuploidy during early development.