Cultivated potato (Solanum tuberosum L.) is a highly heterozygous and clonally propagated autotetraploid (2n=4x=48) that exhibits severe inbreeding depression. These attributes of potato make improvement through conventional breeding difficult and slow, and have motivated development of alternative approaches. One attractive approach is to reinvent potato as a diploid, inbred line-based crop by capturing elite tetraploid germplasm at the diploid level via haploid induction. In potato, haploid induction is routinely achieved by pollination with specialized haploid inducer lines, which operate by an undetermined mechanism. Genome editing represents another attractive approach. Currently, editing requires regeneration of individually edited cells into plants, which has long been known to destabilize the genome. An improved understanding of the biological processes underlying haploid induction and genome instability could aid in techniques to improve potato that may be broadly applicable in plants. Studies were conducted to better understand the frequency, extent and underlying basis of genome instability in potato haploid induction or tissue culture regeneration. Sequencing the genomes of 1,086 primary dihaploids revealed whole-chromosome aneuploidy in 8% of progeny. In the majority of cases, aneuploidy was a single additional chromosome from the tetraploid maternal parent, likely a result of meiotic nondisjunction. Chromosomes from the haploid inducer parent were detected in 0.5% of progeny and showed evidence of restructuring. Among progeny with additional chromosomes from the haploid inducer, additional inducer-derived DNA segments were detected, but their location could not be precisely determined, and in some cases, were artifacts of reference genome assembly. Genome sequencing of 134 triploid or tetraploid hybrids obtained from potato haploid induction crosses revealed ploidy-dependent genome instability of the haploid inducer parent: inducer chromosomes were stable in triploids, but not in tetraploids. Tetraploid hybrids could be produced by several possible mechanisms, but most were produced by first meiotic division restitution of the haploid inducer. This study revealed that fertilization can occur in potato haploid induction, ruling out parthenogenesis as an exclusive mechanism; however, the vast majority of primary dihaploids were free of detectable haploid inducer DNA. In light of these findings, the incidental transfer of haploid inducer DNA to primary dihaploids, which was once thought to be both pervasive and undesirable for potato breeding, occurs infrequently. Analysis of 12 leaf protoplast regenerants from a single tetraploid cultivar revealed a preexisting unbalanced translocation, tr8-7, in the protoplast donor. Genetic and cytogenetic analyses indicated that tr8-7 is the derived state within the protoplast donor, and that cells carrying tr8-7 compose the L2 and L3 cell layers of the shoot apical meristem. Regeneration also led to whole-chromosome aneuploidy, copy-neutral change of heterozygosity consistent with chromosome substitution, as well as catastrophic chromosome shattering similar to that observed in cancer genomes. These findings provide a framework for studying somatic mutations in long-lived and/or polyploid plants and provide further evidence of the destabilizing effect of tissue culture regeneration.