The pivotal role of lysosomes in cellular processes is increasingly appreciated. An understanding of the balanced interplay between the activity of acidic hydrolases, lysosomal membrane proteins and cytosolic proteins is required. Lysosomal storage diseases (LSDs) are characterized by disturbances in this network and by intralysosomal accumulation of substrates, often only in certain cell types. Even though our knowledge of these diseases has increased and therapies have been established, many aspects of the molecular pathology of LSDs remain obscure. This Review aims to discuss how lysosomal storage affects functions linked to lysosomes, such as membrane repair, autophagy, exocytosis, lipid homeostasis, signalling cascades and cell viability. Therapies must aim to correct lysosomal storage not only morphologically, but reverse its (patho)biochemical consequences. As different LSDs have different molecular causes, this requires custom tailoring of therapies. We will discuss the major advantages and drawbacks of current and possible future therapies for LSDs. Study of the pathological molecular mechanisms underlying these 'experiments of nature' often yields information that is relevant for other conditions found in the general population. Therefore, more common diseases may profit from a correction of impaired lysosomal function.