Biofilms are complex structures formed by bacteria, fungi, or even viruses on biotic and abiotic surfaces, and they can be found in almost any part of the human body. The prevalence of biofilm-associated diseases has increased in recent years, mainly because of the frequent use of indwelling medical devices that create opportunities for clinically important bacteria and fungi to form biofilms either on the device or on the neighboring tissues. As a result of their resistance to antibiotics and host immunity factors, biofilms have been associated with the development or persistence of several clinically important diseases. The inability to completely eradicate biofilms drastically increases the burden of disease on both the patient and the healthcare system. Therefore, it is crucial to develop innovative ways to tackle the growth and development of biofilms. This review focuses on dental- and implant-associated biofilm infections, their prevalence in humans, and potential therapeutic intervention strategies, including the recent advances in pharmacology and biomedical engineering. It lists current strategies used to control the formation of clinically important biofilms, including novel antibiotics and their carriers, antiseptics and disinfectants, small molecule anti-biofilm agents, surface treatment strategies, and nanostructure functionalization, as well as multifunctional coatings particularly suitable for providing antibacterial effects to the surface of implants, to treat either dental- or implant-related bacterial infections.