Host-cell invasion by apicomplexan parasites is a unique process that is powered by the gliding motility motor and requires a transmembrane link between the parasite cytoskeleton and the host cell. The thrombospondin-related anonymous protein (TRAP) from Plasmodium plays such a part during sporozoite invasion by linking to actin through its cytoplasmic tail while binding to hepatocytes via its extracellular portion. In recent years, there have been major advances in the identification and characterization of TRAP-family proteins in the other invasive stages of Plasmodium as well as other Apicomplexa. This review summarizes the recent experimental data on these TRAP-family proteins, focusing on their structure and function.