Despite remarkable advances in our understanding of the drivers of human malignancies, new targeted therapies often fail to show sufficient efficacy in clinical trials. Indeed, the cost of bringing a new agent to market has risen substantially in the last several decades, fuelled partly by lack of efficacy in late phase clinical trials. Even in cases where a new agent is deemed 'successful', the development of resistance is often seen as inevitable and clinical responses can be fleeting. Typically, resistance to targeted therapies is thought to arise from pre-existing populations within the tumour, rather than from de novo evolution, yet few studies have experimentally tested this understanding. Indeed, recent reports in the literature have described epigenetically regulated drug tolerant populations within cancers, defined by cell-cycle regulation and/or quiescent repopulation dynamics, drug induced chromatin remodelling or differential transcription factor binding, that can be transient or permanent in nature. This thesis will outline experiments using high complexity molecular barcodes to trace the fate of individual cellular clones in the development of drug resistance. With this technique, cellular clones can be uncoupled from their genomic backgrounds, giving a new depth to our understanding of clonal selection in cancer. In particular, high complexity barcodes are used to identify a pre-existing tamoxifen resistant population in the MCF7 cell line. This resistance phenotype is then linked to the induction of embryonic transcription factor OCT4. Finally, we use our molecular barcoding technique to interrogate the repopulation dynamics of a breast cancer PDX model, supporting their use as complex model systems suitable for studying the origins and consequences of tumour heterogeneity.