Trophically-transmitted parasites are known for their ability to enhance predation of their intermediate host but they are less known for their ability to suppress predation. We review recent literature on host manipulation explaining why and when in its life cycle a parasite benefits from preventing the predation of its host. Predation suppression occurs in intermediate hosts as long as the parasite larva has not reached the developmental conditions allowing it to successfully establish in the next host (competency). We also examine the possibility that predation suppression may occur in hosts harbouring competent larvae (post competency) since some parasites have been shown to manipulate host behaviour in a way that decreases the risk of parasite death through non-host predation (i.e. the consumption of its intermediate host by a predator that does not risk infection). Predation suppression when the parasite is competent has to be considered with respect to non-host predation risk and is not mutually exclusive with predation enhancement. We use the recent theoretical advances in host manipulation to investigate the conditions under which predation suppression could evolve post competency.