Background: All diseases containing genetic material undergo genetic evolution and give rise to heterogeneity including cancer and infection. Although these illnesses are biologically very different, the ability for phylogenetic retrodiction based on the genomic reads is common between them and thus tree-based principles and assumptions are shared. Just as the different frequencies of tumor genomic variants presupposes the existence of multiple tumor clones and provides a handle to computationally infer them, we postulate that the different variant frequencies in viral reads offers the means to infer multiple co-infecting sublineages. Results: We present a common methodological framework to infer the phylogenomics from genomic data, be it reads of SARS-CoV-2 of multiple COVID-19 patients or bulk DNAseq of the tumor of a cancer patient. We describe the Concerti computational framework for inferring phylogenies in each of the two scenarios.To demonstrate the accuracy of the method, we reproduce some known results in both scenarios. We also make some additional discoveries. Conclusions: Concerti successfully extracts and integrates information from multi-point samples, enabling the discovery of clinically plausible phylogenetic trees that capture the heterogeneity known to exist both spatially and temporally. These models can have direct therapeutic implications by highlighting “birth” of clones that may harbor resistance mechanisms to treatment, “death” of subclones with drug targets, and acquisition of functionally pertinent mutations in clones that may have seemed clinically irrelevant. Specifically in this paper we uncover new potential parallel mutations in the evolution of the SARS-CoV-2 virus. In the context of cancer, we identify new clones harboring resistant mutations to therapy.