Malaria is still the most destructive and dangerous parasitic infection in many tropical and subtropical countries. The burden of this disease is getting worse, mainly due to the increasing resistance of Plasmodium falciparum against the widely available antimalarial drugs. There is an urgent need for new, more affordable and accessible antimalarial agents possessing original modes of action. Natural products have played a dominant role in the discovery of leads for the development of drugs to treat human diseases, and this fact anticipates that new antimalarial leads may certainly emerge from tropical plant sources. This present review covers most of the recently-published non-alkaloidal natural compounds from plants with antiplasmodial and antimalarial properties, belonging to the classes of terpenes, limonoids, flavonoids, chromones, xanthones, anthraquinones, miscellaneous and related compounds, besides the majority of papers describing antiplasmodial crude extracts published in the last five years not reviewed before. In addition, some perspectives and remarks on the development of new drugs and phytomedicines for malaria are succinctly discussed.