Polyploids are species in which three or more sets of chromosomes coexist. Polyploidy frequently occurs in plants and plays a major role in their evolution. Based on their origin, polyploid species can be divided into two groups: autopolyploids and allopolyploids. The autopolyploids arise by multiplication of the chromosome sets from a single species, whereas allopolyploids emerge from the hybridization between distinct species followed or preceded by whole genome duplication, leading to the combination of divergent genomes. Having a polyploid constitution offers some fitness advantages, which could become evolutionarily successful. Nevertheless, polyploid species must develop mechanism(s) that control proper segregation of genetic material during meiosis, and hence, genome stability. Otherwise, the coexistence of more than two copies of the same or similar chromosome sets may lead to multivalent formation during the first meiotic division and subsequent production of aneuploid gametes. In this review, we aim to discuss the pathways leading to the formation of polyploids, the occurrence of polyploidy in the grass family (Poaceae), and mechanisms controlling chromosome associations during meiosis, with special emphasis on wheat.