Oocyte/embryo selection methodologies are either invasive or noninvasive and can be applied at various stages of development from the oocyte to cleaved embryos and up to the blastocyst stage. Morphology and the proportion of embryos developing to the blastocyst stage are important criteria to assess developmental competence. Evaluation of morphology remains the method of choice for selecting viable oocytes for IVP or embryos prior to transfer. Although non-invasive approaches are improving, invasive ones have been extremely helpful in finding candidate genes to determine oocyte/embryo quality. There is still a strong need for further refinement of existing oocyte and embryo selection methods and quality parameters. The development of novel, robust and non-invasive procedures will ensure that only embryos with the highest developmental potential are chosen for transfer. In the present review, various methods for assessing the quality of oocytes and preimplantation embryos, particularly in cattle, are considered. These methods include assessment of morphology including different staining procedures, transcriptomic and proteomic analyses, metabolic profiling, as well as the use of artificial intelligence technologies.