Systematic sequencing of cancer genomes has revealed prevalent heterogeneity, with patients harboring various combinatorial patterns of genetic alteration. In particular, a phenomenon that a group of genes exhibits mutually exclusive patterns has been widespread across cancers, covering a broad spectrum of crucial cancer pathways. Recently, there is considerable evidence showing that, mutual exclusivity reflects alternative functions in tumor initiation and progression, or suggests adverse effects of their concurrence. Given its importance, numerous computational approaches have been proposed to study mutual exclusivity using genomic profiles alone, or by integrating networks and phenotypes. Some of them have been routinely used to explore genetic associations, which lead to a deeper understanding of carcinogenic mechanisms and reveals unexpected tumor vulnerabilities. Here, we present an overview of mutual exclusivity from the perspective of cancer genome. We describe the common hypothesis underlying mutual exclusivity, summarize the strategies for the identification of significant mutually exclusive patterns, compare the performance of representative algorithms from simulated data sets and discuss their common confounders.