Autophagy is the major intracellular machinery for degrading proteins, lipids, polysaccharides, and organelles. This cellular process is essential for the maintenance of the correct cellular balance in both physiological and stress conditions. Because of its role in maintaining cellular homeostasis, dysregulation of autophagy leads to various disease manifestations, such as inflammation, metabolic alterations, aging, and neurodegeneration. A common feature of many neurologic and neuromuscular diseases is the alteration of the autophagy-lysosomal pathways. For this reason, autophagy is considered a target for the prevention and/or cure of these diseases. Dietary intake of polyphenols has been demonstrated to prevent/ameliorate several of these diseases. Thus, natural products that can modulate the autophagy machinery are considered a promising therapeutic strategy. In particular, curcumin, a phenolic compound widely used as a dietary supplement, exerts an important effect in modulating autophagy. Herein, we report on the current knowledge concerning the role of curcumin in modulating the autophagy machinery in various neurological and neuromuscular diseases as well as its role in restoring the autophagy molecular mechanism in several cell types that have different effects on the progression of neurological and neuromuscular disorders.