Cell repair machinery is responsible for protecting the genome from endogenous and exogenous effects that induce DNA damage. Mutations that occur in somatic cells lead to dysfunction in certain tissues or organs, while a violation of genomic integrity during the embryonic period often leads to death. A mammalian embryo’s ability to respond to damaged DNA and repair it, as well as its sensitivity to specific lesions, is still not well understood. In this review, we combine disparate data on repair processes in the early stages of preimplantation development in mammalian embryos.