Apomixis is desirable in agriculture as a reproductive strategy for cloning plants by seeds. Because embryos derive from the parthenogenic development of apomeiotic egg cells, apomixis excludes fertilization in addition to meiotic segregation and recombination, resulting in offspring that are exact replicas of the parent. Introgression of apomixis from wild relatives to crop species and transformation of sexual genotypes into apomictically reproducing ones are long-held goals of plant breeding. In fact, it is generally accepted that the introduction of apomixis into agronomically important crops will have revolutionary implications for agriculture. This review deals with the current genetic and molecular findings that have been collected from model species to elucidate the mechanisms of apomeiosis, parthenogenesis and apomixis as a whole. Our goal is to critically determine whether biotechnology can combine key genes known to control the expression of the processes miming the main components of apomixis in plants. Two natural apomicts, as the eudicot Hypericum perforatum L. (St. John’s wort) and the monocot Paspalumspp. (crowngrass), and the sexual model species Arabidopsis thaliana are ideally suited for such investigations at the genomic and biotechnological levels. Some novel views and original concepts have been faced on this review, including (i) the parallel between Y-chromosome and apomixis-bearing chromosome (e.g., comparative genomic analyses revealed common features as repression of recombination events, accumulation of transposable elements and degeneration of genes) from the most primitive (Hypericum-type) to the most advanced (Paspalum-type) in evolutionary terms, and (ii) the link between apomixis and gene-specific silencing mechanisms (i.e., likely based on chromatin remodelling factors), with merging lines of evidence regarding the role of auxin in cell fate specification of embryo sac and egg cell development in Arabidopsis. The production of engineered plants exhibiting apomictic-like phenotypes is critically reviewed and discussed.