The leukodystrophies are a group of genetic metabolic diseases characterized by an abnormal development or progressive degeneration of the myelin sheath. The myelin is a complex sheath composed of several macromolecules covering axons as an insulator. Each of the leukodystrophies is caused by mutations in genes encoding enzymes that are involved in myelin production and maintenance. The lysosomal storage diseases are inborn disorders of compartmentalized cellular organelles with broad clinical manifestations secondary to the progressive accumulation of undegraded macromolecules within lysosomes and related organelles. The more than 60 different lysosomal storage diseases are rare diseases; however, collectively, the incidence of lysosomal storage diseases ranges just over 1 in 2500 live births. The majority of lysosomal storage diseases are associated with neurologic manifestations including developmental delay, seizures, acroparesthesia, motor weakness, and extrapyramidal signs. These inborn organelle disorders show wide clinical variability affecting individuals from all age groups. In addition, several of neurologic, also known as neuronopathic, lysosomal storage diseases are associated with some level of white matter disease, which often triggers the diagnostic investigation. Most lysosomal storage diseases are autosomal recessively inherited and few are X-linked, with females being at risk of presenting with mild, but clinically relevant neurologic manifestations. Biochemical assays are the basis of the diagnosis and are usually confirmed by molecular genetic testing. Novel therapies have emerged. However, most affected patients with lysosomal storage diseases have only supportive management to rely on. A better understanding of the mechanisms resulting in the leukodystrophy will certainly result in innovative and efficacious disease-modifying therapies.