Protozoan parasites have developed elaborate motility systems that facilitate infection and dissemination. For example, amoebae use actin-rich membrane extensions called pseudopodia, whereas Kinetoplastida are propelled by microtubule-containing flagella. By contrast, the motile and invasive stages of the Apicomplexa - a phylum that contains the important human pathogens Plasmodium falciparum (which causes malaria) and Toxoplasma gondii (which causes toxoplasmosis) - have a unique machinery called the glideosome, which is composed of an actomyosin system that underlies the plasma membrane. The glideosome promotes substrate-dependent gliding motility, which powers migration across biological barriers, as well as active host cell entry and egress from infected cells. In this Review, we discuss the discovery of the principles that govern gliding motility, the characterization of the molecular machinery involved, and its impact on parasite invasion and egress from infected cells.