Polyploidy, the genome wide duplication of chromosome number, is a key feature in eukaryote evolution. Polyploidy exists in diverse groups including animals, fungi, and invertebrates but is especially prevalent in plants with most, if not all, plant species having descended from a polyploidization event. Polyploids often differ markedly from their diploid progenitors in morphological, physiological, and life history characteristics as well as rates of adaptation. The altered characteristics displayed by polyploids may contribute to their success in novel ecological habitats. Clearly, a better understanding of the processes underlying changes in the number of chromosomes within genomes is a key goal in our understanding of speciation and adaptation for a wide range of families and genera. Despite the fundamental role of chromosome number change in eukaryotic evolution, probabilistic models describing the evolution of chromosome number along a phylogeny have not yet been formulated. We present a series of likelihood models, each representing a different hypothesis regarding the evolution of chromosome number along a given phylogeny. These models allow us to reconstruct ancestral chromosome numbers and to estimate the expected number of polyploidization events and single chromosome changes (dysploidy) that occurred along a phylogeny. We test, using simulations, the accuracy of this approach and its dependence on the number of taxa and tree length. We then demonstrate the application of the method for the study of chromosome number evolution in 4 plant genera: Aristolochia, Carex, Passiflora, and Helianthus. Considering the depth of the available cytological and phylogenetic data, formal models of chromosome number evolution are expected to advance significantly our understanding of the importance of polyploidy and dysploidy across different taxonomic groups.