Triple-negative breast cancer (TNBC) is a highly heterogeneous disease that encompasses a subset of breast cancers that are defined by the absence of expression of the estrogen receptor, the progesterone receptor, and human epidermal growth factor receptor 2 (HER2, ERBB2). Among all breast cancer subtypes, TNBC is associated with the least favorable prognosis because of its aggressive clinical course and long-standing lack of effective targeted therapies. Recently, multi-omics profiling studies have provided unprecedented insights into the biological heterogeneity of TNBC, leading to the classification of these tumors into distinct molecular subtypes based on recurrent genetic aberrations, transcriptional patterns, and tumor microenvironment features. A significant number of kinase-driven molecular alterations have been identified across TNBC molecular subtypes, opening new possibilities for refining and broadening the current therapeutic landscape. Many small-molecule inhibitors of protein kinases have been tested in clinical trials in patients with TNBC, including drugs that target the PI3K/Akt/mTOR and MAPK signaling pathways, receptor tyrosine kinases, cyclin-dependent kinases, and DNA damage response signaling pathways. Although some of these agents had limited efficacy in an unselected population of TNBC patients, recent studies suggest that kinase inhibitors may provide significant clinical benefits in the framework of subtype-based and biomarker-guided therapeutic approaches. This review explores actionable therapeutic targets for TNBC molecular subtypes and describes recent clinical trials that investigated kinase inhibitors in the treatment of triple-negative breast tumors.