Intratumoral heterogeneity can exist along multiple axes: Cancer stem cells (CSCs)/non-CSCs, drug-sensitive/drug-tolerant states, and a spectrum of epithelial–hybrid–mesenchymal phenotypes. Further, these diverse cell-states can switch reversibly among one another, thereby posing a major challenge to therapeutic efficacy. Therefore, understanding the origins of phenotypic plasticity and heterogeneity remains an active area of investigation. While genomic components (mutations, chromosomal instability) driving heterogeneity have been well-studied, recent reports highlight the role of non-genetic mechanisms in enabling both phenotypic plasticity and heterogeneity. Here, we discuss various processes underlying phenotypic plasticity such as stochastic gene expression, chromatin reprogramming, asymmetric cell division and the presence of multiple stable gene expression patterns (‘attractors’). These processes can facilitate a dynamically evolving cell population such that a subpopulation of (drug-tolerant) cells can survive lethal drug exposure and recapitulate population heterogeneity on drug withdrawal, leading to relapse. These drug-tolerant cells can be both pre-existing and also induced by the drug itself through cell-state reprogramming. The dynamics of cell-state transitions both in absence and presence of the drug can be quantified through mathematical models. Such a dynamical systems approach to elucidating patterns of intratumoral heterogeneity by integrating longitudinal experimental data with mathematical models can help design effective combinatorial and/or sequential therapies for better clinical outcomes.