Polyploidy can have a huge impact on the evolution of species, and it is a common occurrence, especially in plants. The two types of polyploids-autopolyploids and allopolyploids-differ in the level of divergence between the genes that are brought together in the new polyploid lineage. Because allopolyploids are formed via hybridization, the homoeologous copies of genes within them are at least as divergent as orthologs in the parental species that came together to form them. This means that common methods for estimating the parental lineages of allopolyploidy events are not accurate, and can lead to incorrect inferences about the number of gene duplications and losses. Here, we have adapted an algorithm for topology-based gene-tree reconciliation to work with multi-labeled trees (MUL-trees). By definition, MUL-trees have some tips with identical labels, which makes them a natural representation of the genomes of polyploids. Using this new reconciliation algorithm we can: accurately place allopolyploidy events on a phylogeny, identify the parental lineages that hybridized to form allopolyploids, distinguish between allo-, auto-, and (in most cases) no polyploidy, and correctly count the number of duplications and losses in a set of gene trees. We validate our method using gene trees simulated with and without polyploidy, and revisit the history of polyploidy in data from the clades including both baker's yeast and bread wheat. Our re-analysis of the yeast data confirms the allopolyploid origin and parental lineages previously identified for this group. The method presented here should find wide use in the growing number of genomes from species with a history of polyploidy. [Polyploidy; reconciliation; whole-genome duplication.].