Curcumin, a hydrophobic polyphenol extracted from the rhizome of Curcuma longa, is now considered a candidate drug for the treatment of neurological diseases, including Parkinson’s Disease (PD), Alzheimer’s Disease (AD), Huntington’s Disease (HD), Multiple Sclerosis (MS), Amyotrophic Lateral Sclerosis (ALS), and prion disease, due to its potent anti-inflammatory, antioxidant potential, anticancerous, immunomodulatory, neuroprotective, antiproliferative, and antibacterial activities. Traditionally, curcumin has been used for medicinal and dietary purposes in Asia, India, and China. However, low water solubility, poor stability in the blood, high rate of metabolism, limited bioavailability, and little capability to cross the blood–brain barrier (BBB) have limited the clinical application of curcumin, despite the important pharmacological activities of this drug. A variety of nanocarriers, including liposomes, micelles, dendrimers, cubosome nanoparticles, polymer nanoparticles, and solid lipid nanoparticles have been developed with great success to effectively deliver the active drug to brain cells. Functionalization on the surface of nanoparticles with brain-specific ligands makes them target-specific, which should significantly improve bioavailability and reduce harmful effects. The aim of this review is to summarize the studies on curcumin and/or nanoparticles containing curcumin in the most common neurodegenerative diseases, highlighting the high neuroprotective potential of this nutraceutical.