Genomic patterns of diversity and divergence are impacted by certain life history traits, reproductive systems, and demographic history. The latter is characterized by fluctuations in population sizes over time, as well as by temporal patterns of introgression. For a given organism, identifying a demographic history that deviates from the standard neutral model allows a better understanding of its evolution but also helps to reduce the risk of false positives when screening for molecular targets of natural selection. Tetraploid organisms and beyond have demographic histories that are complicated by the mode of polyploidization, the mode of inheritance, and different scenarios of gene flow between sub-genomes and diploid parental species. Here we provide guidelines for experimenters wishing to address these issues through a flexible statistical framework: approximate Bayesian computation (ABC). The emphasis is on the general philosophy of the approach to encourage future users to exploit the enormous flexibility of ABC beyond the limitations imposed by generalist data analysis pipelines.