Cancer is often driven by the accumulation of genetic alterations, including single nucleotide variants, small insertions or deletions, gene fusions, copy-number variations, and large chromosomal rearrangements. Recent advances in next-generation sequencing technologies have helped investigators generate massive amounts of cancer genomic data and catalog somatic mutations in both common and rare cancer types. So far, the somatic mutation landscapes and signatures of >10 major cancer types have been reported; however, pinpointing driver mutations and cancer genes from millions of available cancer somatic mutations remains a monumental challenge. To tackle this important task, many methods and computational tools have been developed during the past several years and, thus, a review of its advances is urgently needed. Here, we first summarize the main features of these methods and tools for whole-exome, whole-genome and whole-transcriptome sequencing data. Then, we discuss major challenges like tumor intra-heterogeneity, tumor sample saturation and functionality of synonymous mutations in cancer, all of which may result in false-positive discoveries. Finally, we highlight new directions in studying regulatory roles of noncoding somatic mutations and quantitatively measuring circulating tumor DNA in cancer. This review may help investigators find an appropriate tool for detecting potential driver or actionable mutations in rapidly emerging precision cancer medicine.