During healthy development and aging, somatic mutations aggregate in tissues, lending different mutational profiles to cells within these tissues. Similarly, developmental processes create the functional diversity necessary for normal tissue function. Cancer arises from the aberrant functioning of these processes. Mutational profiles and epigenetic regulation support uncontrolled growth of neoplasms with the potential ability to invade nearby tissues. The resulting intra-tumor heterogeneity contributes to evasion of drug pressures via Darwinian selection, and cell-state plasticity allows for dynamic shifts in regulation into drug-resistant persistor states. While bulk genomic assays profile averages of sampled cell populations, single-cell approaches allow for a picture of the heterogeneity of healthy and diseased complex tissues. In this dissertation, I assess the state of the single-cell field with a focus on assays characterizing whole genome copy number variation and chromatin accessibility. I show three examples of profiling heterogeneity by (i) assessing the genomes of thousands of cells in healthy and diseased tissues (ii) mapping the chromatin landscape of the murine hippocampus, and (iii) characterizing the development of Trametinib resistance through cell state plasticity across basal-like triple negative breast cancer cell lines.