Salivary gland neoplasms are a morphologically heterogenous group of lesions that are often diagnostically challenging. In recent years, considerable progress in salivary gland taxonomy has been reached by the discovery of tumor type-specific fusion oncogenes generated by chromosome translocations. This review describes the clinicopathologic features of a selected group of salivary gland carcinomas with a focus on their distinctive genomic characteristics. Mammary analog secretory carcinoma is a recently described entity characterized by a t(12;15)(p13;q25) translocation resulting in an ETV6-NTRK3 fusion. Hyalinizing clear cell carcinoma is a low-grade tumor with infrequent nodal and distant metastasis, recently shown to harbor an EWSR1-ATF1 gene fusion. The CRTC1-MAML2 fusion gene resulting from a t(11;19)(q21;p13) translocation, is now known to be a feature of both low-grade and high-grade mucoepidermoid carcinomas associated with improved survival. A t(6;9)(q22-23;p23-34) translocation resulting in a MYB-NFIB gene fusion has been identified in the majority of adenoid cystic carcinomas. Polymorphous (low-grade) adenocarcinoma and cribriform adenocarcinoma of (minor) salivary gland origin are related entities with partly differing clinicopathologic and genomic profiles; they are the subject of an ongoing taxonomic debate. Polymorphous (low-grade) adenocarcinomas are characterized by hot spot point E710D mutations in the PRKD1 gene, whereas cribriform adenocarcinoma of (minor) salivary glands origin are characterized by translocations involving the PRKD1-3 genes. Salivary duct carcinoma (SDC) is a high-grade adenocarcinoma with morphologic and molecular features akin to invasive ductal carcinoma of the breast, including HER2 gene amplification, mutations of TP53, PIK3CA, and HRAS and loss or mutation of PTEN. Notably, a recurrent NCOA4-RET fusion has also been found in SDC. A subset of SDC with apocrine morphology is associated with overexpression of androgen receptors. As these genetic aberrations are recurrent they serve as powerful diagnostic tools in salivary gland tumor diagnosis, and therefore also in refinement of salivary gland cancer classification. Moreover, they are promising as prognostic biomarkers and targets of therapy.