Metals—especially iron, copper and manganese—are important elements of brain functions and development. Metal-dysregulation homeostasis is associated with brain-structure damage to the motor, cognitive and emotional systems, and leads to neurodegenerative processes. There is more and more evidence that specialized cognitive and motor exercises can enhance brain function and attenuate neurodegeneration in mechanisms, such as improving neuroplasticity by altering the synaptic structure and function in many brain regions. Psychological and physical methods of rehabilitation are now becoming increasingly important, as pharmacological treatments for movement, cognitive and emotional symptoms are limited. The present study describes physical and cognitive rehabilitation methods of patients associated with metal-induced neurotoxicity such as Alzheimer’s disease, Parkinson’s disease, amyotrophic lateral sclerosis, Huntington’s disease and Wilson’s disease. In our review, we describe physical (e.g., virtual-reality environments, robotic-assists training) and psychological (cognitive training, cognitive stimulation, neuropsychological rehabilitation and cognitive-behavioral and mindfulness-based therapies) methods, significantly improving the quality of life and independence of patients associated with storage diseases. Storage diseases are a diverse group of hereditary metabolic defects characterized by the abnormal cumulation of storage material in cells. This topic is being addressed due to the fact that rehabilitation plays a vital role in the treatment of neurodegenerative diseases. Unfortunately so far there are no specific guidelines concerning physiotherapy in neurodegenerative disorders, especially in regards to duration of exercise, type of exercise and intensity, as well as frequency of exercise. This is in part due to the variety of symptoms of these diseases and the various levels of disease progression. This further proves the need for more research to be carried out on the role of exercise in neurodegenerative disorder treatment.