Cancer driver genes are either oncogenes or tumour suppressor genes that are classically activated or inactivated, respectively, by driver mutations. Alternative splicing—which produces various mature mRNAs and, eventually, protein variants from a single gene—may also result in driving neoplastic transformation because of the different and often opposed functions of the variants of driver genes. The present review analyses the different alternative splicing events that result in driving neoplastic transformation, with an emphasis on their molecular mechanisms. To do this, we collected a list of 568 gene drivers of cancer and revised the literature to select those involved in the alternative splicing of other genes as well as those in which its pre-mRNA is subject to alternative splicing, with the result, in both cases, of producing an oncogenic isoform. Thirty-one genes fall into the first category, which includes splicing factors and components of the spliceosome and splicing regulators. In the second category, namely that comprising driver genes in which alternative splicing produces the oncogenic isoform, 168 genes were found. Then, we grouped them according to the molecular mechanisms responsible for alternative splicing yielding oncogenic isoforms, namely, mutations in cis splicing-determining elements, other causes involving non-mutated cis elements, changes in splicing factors, and epigenetic and chromatin-related changes. The data given in the present review substantiate the idea that aberrant splicing may regulate the activation of proto-oncogenes or inactivation of tumour suppressor genes and details on the mechanisms involved are given for more than 40 driver genes.