With the growing use of dental implants, the incidence of implants' failures grows. Late treatment complications, after reaching full osseointegration and functionality, include mechanical failures, such as fracture of the implant and its components. Those complications are deemed severe in dentistry, albeit being usually considered as rare, and therefore seldom addressed in the clinical literature. The introduction of dental implants into clinical practice fostered a wealth of research on their biological aspects. By contrast, mechanical strength and reliability issues were seldom investigated in the open literature, so that most of the information to date remains essentially with the manufacturers. Over the years, implants have gone through major changes regarding the material, the design, and the surface characteristics aimed at improving osseointegration. Did those changes improve the implants' mechanical performance? This review article surveys the state-of-the-art literature about implants' mechanical reliability, identifying the known causes for fracture, while outlining the current knowledge-gaps. Recent results on various aspects of the mechanical integrity and failure of implants are presented and discussed next. The paper ends by a general discussion and suggestions for future research, outlining the importance of mechanical considerations for the improvement of their future performance.