Neurodegenerative diseases are characterized by irreversible cell damage, loss of neuronal cells and limited regeneration potential of the adult nervous system. Pluripotent stem cells are capable of differentiating into the multitude of cell types that compose the central and peripheral nervous systems and so have become the major focus of cell replacement therapies for the treatment of neurological disorders. Human embryonic stem cell (hESC) and human induced pluripotent stem cell (hiPSC)-derived cells have both been extensively studied as cell therapies in a wide range of neurodegenerative disease models in rodents and non-human primates, including Parkinson’s disease, stroke, epilepsy, spinal cord injury, Alzheimer’s disease, multiple sclerosis and pain. In this review, we discuss the latest progress made with stem cell therapies targeting these pathologies. We also evaluate the challenges in clinical application of human pluripotent stem cell (hPSC)-based therapies including risk of oncogenesis and tumor formation, immune rejection and difficulty in regeneration of the heterogeneous cell types composing the central nervous system.