Approximately 50% of melanomas harbor an activating BRAF mutation. Combined BRAF and MEK inhibitors such as dabrafenib and trametinib, vemurafenib and cobimetinib, and encorafenib and binimetinib are US Food and Drug Administration (FDA)-approved to treat patients with BRAF^V600-mutated advanced melanoma. Both genetic and epigenetic alterations play a major role in resistance to BRAF inhibitors by reactivation of the MAPK and/or the PI3K–Akt pathways. The role of BRAF inhibitors in modulating the immunomicroenvironment and perhaps enhancing the efficacy of checkpoint inhibitors is gaining interest. This article provides a comprehensive review of mechanisms of resistance to BRAF and MEK inhibitors in melanoma and summarizes landmark trials that led to the FDA approval of BRAF and MEK inhibitors in metastatic melanoma.