One of the key challenges of cancer biology is to catalogue and understand the somatic genomic alterations leading to cancer. Although alternative definitions and search methods have been developed to identify cancer driver genes and mutations, analyses of thousands of cancer genomes return a remarkably similar catalogue of around 300 genes that are mutated in at least one cancer type. Yet, many features of these genes and their role in cancer remain unclear, first and foremost when a somatic mutation is truly oncogenic. In this review, we first summarize some of the recent efforts in completing the catalogue of cancer driver genes. Then, we give an overview of different aspects that influence the oncogenicity of somatic mutations in the core cancer driver genes, including their interactions with the germline genome, other cancer driver mutations, the immune system, or their potential role in healthy tissues. In the coming years, this research holds promise to illuminate how, when, and why cancer driver genes and mutations are really drivers, and thereby move personalized cancer medicine and targeted therapies forward.