Skeletal muscle mass, a strong predictor of longevity and health in humans, is determined by the balance of two cellular processes, muscle protein synthesis (MPS) and muscle protein breakdown. MPS seems to be particularly sensitive to changes in mechanical load and/or nutritional status; therefore, much research has focused on understanding the molecular mechanisms that underpin this cellular process. Furthermore, older individuals display an attenuated MPS response to anabolic stimuli, termed anabolic resistance, which has a negative impact on muscle mass and function, as well as quality of life. Therefore, an understanding of which, if any, molecular mechanisms contribute to anabolic resistance of MPS is of vital importance in formulation of therapeutic interventions for such populations. This review summarizes the current knowledge of the mechanisms that underpin MPS, which are broadly divided into mechanistic target of rapamycin complex 1 (mTORC1)-dependent, mTORC1-independent, and ribosomal biogenesis-related, and describes the evidence that shows how they are regulated by anabolic stimuli (exercise and/or nutrition) in healthy human skeletal muscle. This review also summarizes evidence regarding which of these mechanisms may be implicated in age-related skeletal muscle anabolic resistance and provides recommendations for future avenues of research that can expand our knowledge of this area.