The study of genomic variation is vital for our understanding of the gene dosage changes which occur widely in cancer. These dosage changes are a key alteration to the cancer cell whereby tumours bypass protective cellular mechanisms in order to grow and proliferate. In order to accurately determine the gene dosage changes in a representative range of cancers we used sequencing data for the NCI-60 cell lines to create a high-resolution map of copy number variants (CNVs). Our analysis of CNV hotspots in the cancer genome suggests novel candidate cancer driver genes. These driver genes are enriched for roles in proliferation, angiogenesis and apoptosis, consistent with the hypothesis that tumour cells must escape various protective mechanisms before they gain the hallmarks of cancer. The presence of paralogs associated with heritable dominant diseases in the human genome is a paradox, since purifying selection would be expected to remove them, and yet they are found throughout the metazoa. To study the role of whole genome duplications (WGDs) in the persistence of these disease-associated genes we implemented a new gene dating method, which provides a more detailed perspective on gene duplications than has been previously possible. We propose that the WGDs in the vertebrate ancestor led to a switch from recessive to dominant disease specifically because of the haploinsufficiency of the retained ohnologs, rather than due to more general dosage sensitivity. Tumour cells survive gene dosage alterations which are lethal to normal cells, so buffering mechanisms such as miRNAs must be key to these processes. A handful of miRNAs have been annotated with oncogenic and tumour suppressor roles. The most important of these is the mir-17~92 cluster, also called Oncomir-1. We find widespread derepression of cancer- related processes and pathways caused by the frequent loss of tumour suppressor miRNAs, as well as by global miRNA depletion resulting from the disruption of miRNA biogenesis. We propose a novel mechanism whereby transient C-MYC elevation leads to TP53 repression via mir-663a/1228, which then allows Oncomir-1 to repress TP53 and PTEN in a sustained manner. This bistable switch could potentially be reversed with Oncomir-1 antagonists. The work presented in this thesis advances our understanding of the role of miRNAs in buffering gene dosages changes in cancer and points the way to possible new interventions for Oncomir-1-dependent tumours.