Cancer is an evolutionary process involving the accumulation of diverse somatic mutations and clonal evolution over time. Phylogenetic inference from samples obtained from an individual patient offers a powerful approach to unraveling the intricate evolutionary history of cancer and provides insights that can inform cancer treatment. Somatic copy number alterations (CNAs) are important in cancer evolution and are often used as markers, alone or with other somatic mutations, for phylogenetic inferences, particularly in low-coverage DNA sequencing data. Many phylogenetic inference methods using CNAs detected from bulk or single-cell DNA sequencing data have been developed over the years. However, there have been no systematic reviews on these methods. To summarize the state-of-the-art of the field and inform future development, this review presents a comprehensive survey on the major challenges in inference, different types of methods, and applications of these methods. The challenges are discussed from the aspects of input data, models of evolution, and inference algorithms. The different methods are grouped according to the markers used for inference and the types of the reconstructed trees. The applications include using phylogenetic inference to understand intra-tumor heterogeneity, metastasis, treatment resistance, and early cancer development. This review also sheds light on future directions of cancer phylogenetic inference using CNAs, including the improvement of scalability, the utilization of new types of data, and the development of more realistic models of evolution.
