The oocyte is the female germ cell specialized for processing the sperm genome as well as the only cell in the adult body that can convert, i.e., reprogram, the genome of a donor somatic cell from a differentiated to a totipotent state. One of the big open questions in this field pertains to the identity of the natural components of the oocyte that can achieve nuclear reprogramming. We would like to call them determinants of reprogramming. In our view the experimental pursuit of these determinants must be preceded by a review of the oocyte's properties. These can be ascribed to qualitative and quantitative traits such as size, nuclear architecture, cytoplasm-to-nucleus ratio, and molecular makeup of the oocyte. In addition, the oocyte's ability to achieve fast and full reprogramming suggests that the nuclear and/or cytoplasmic molecules in charge of the reprogramming process are abundant. We hypothesize that the reason for such abundance may be simple: these molecules are normally used to process the sperm genome upon fertilization and are repurposed for reprogramming. Among these molecules, maternal-effect factors including transcription factors and chromatin remodeling factors may prime the reprogramming process and determine its initial speed. Here, we discuss known and putative factors involved in reprogramming, such as DJ-1, Brg1, Oct4, Glis1, and Tctp1, that were identified by candidate gene, transcriptomic, and proteomic approaches. Shedding light on the natural network of reprogramming factors found in the oocyte will help reveal general principles of cell rejuvenation for the benefit of aging studies and regenerative medicine.