The advent of single-cell sequencing provides the ability to model the evolution of somatic cells within individuals. For example, inference of cell phylogenies has the potential to advance our understanding of the variation in the process of tumor progression. Phylogenetic methods have been applied in numerous ways to model the evolution of somatic cells from single-cell DNA data using single-nucleotide variants. Some methods implement a finite-sites Markov model by grouping genotypes in various ways, and such models are the focus of this presentation. Since both the maternal and paternal genomes are passed on to daughter cells during mitosis, it is appropriate to start with a phased model of maternal and paternal sequence evolution using a continuous-time Markov process. However, phased genotypes are not always observed, and only unphased genotypes are available. As a result, it is common to group pairs of heterozygous genotypes into single states, leading to an unphased model. Some methods further lump unphased genotypes, resulting in coarser processes. The process with a smaller state space corresponds to a lumped process of the original phased Markov chain and may or may not be Markovian, depending on restrictions imposed on the generator matrix. The purpose of this presentation is to explore the mathematical formulations of phased and unphased Markov processes. We hope to initiate a discussion about whether restrictions should be placed on the generator matrix when inferring tumor phylogenies in practice.