Lysosomes have been classically considered terminal degradative organelles, but in recent years they have been found to participate in many other cellular processes, including killing of intracellular pathogens, antigen presentation, plasma membrane repair, cell adhesion and migration, tumor invasion and metastasis, apoptotic cell death, metabolic signaling and gene regulation. In addition, lysosome dysfunction has been shown to underlie not only rare lysosome storage disorders but also more common diseases, such as cancer and neurodegeneration. The involvement of lysosomes in most of these processes is now known to depend on the ability of lysosomes to move throughout the cytoplasm. Here, we review recent findings on the mechanisms that mediate the motility and positioning of lysosomes, and the importance of lysosome dynamics for cell physiology and pathology.