Salivary gland carcinomas (SGCs) are rare neoplasms, representing less than 10% of all head and neck tumors, but they are extremely heterogeneous from the histological point of view, their clinical behavior, and their genetics. The guidelines regarding their treatment include surgery in most cases, which can also play an important role in oligometastatic disease. Where surgery cannot be used, systemic therapy comes into play. Systemic therapy for many years has been represented by polychemotherapy, but recently, with the affirmation of translational research, it can also count on targeted therapy, at least in some subtypes of SGCs. Interestingly, in some SGC histotypes, predominant mutations have been identified, which in some cases behave as “driver mutations”, namely mutations capable of governing the carcinogenesis process. Targeting these driver mutations may be an effective therapeutic strategy. Nonetheless, it is not always possible to have drugs suitable for targeting driver mutations—and targeting driver mutations is not always accompanied by a clinical benefit. In this review, we will analyze the main mutations predominant in the various histotypes of SGCs.