Naturally occurring autopolyploid species, such as the autotetraploid potato Solanum tuberosum, face a variety of challenges during meiosis. These include proper pairing, recombination and correct segregation of multiple homologous chromosomes, which can form complex multivalent configurations at metaphase I, and in turn alter allelic segregation ratios through double reduction. Here, we present a reference map of meiotic stages in diploid and tetraploid S. tuberosum using fluorescence in situ hybridisation (FISH) to differentiate individual meiotic chromosomes 1 and 2. A diploid-like behaviour at metaphase I involving bivalent configurations was predominant in all three tetraploid varieties. The crossover frequency per bivalent was significantly reduced in the tetraploids compared with a diploid variety, which likely indicates meiotic adaptation to the autotetraploid state. Nevertheless, bivalents were accompanied by a substantial frequency of multivalents, which varied by variety and by chromosome (7–48%). We identified possible sites of synaptic partner switching, leading to multivalent formation, and found potential defects in the polymerisation and/or maintenance of the synaptonemal complex in tetraploids. These findings demonstrate the rise of S. tuberosum as a model for autotetraploid meiotic recombination research and highlight constraints on meiotic chromosome configurations and chiasma frequencies as an important feature of an evolved autotetraploid meiosis.