Mitochondria and chloroplasts both originated from bacterial endosymbionts. The available evidence strongly supports a single origin for mitochondria and only somewhat less strongly a single, slightly later, origin for chloroplasts. The arguments and evidence that have sometimes been presented in favor of the alternative theories of the multiple or polyphyletic origins of these two organelles are evaluated and the kinds of data that are needed to test more rigorously the monophyletic theory are discussed. Although chloroplasts probably originated only once, eukaryotic algae are polyphyletic because chloroplasts have been secondarily transferred to new lineages by the permanent incorporation of a photosynthetic eukaryotic algal cell into a phagotrophic protozoan host. How often this has happened is much less clear. It is particularly unclear whether or not the chloroplasts of typical dinoflagellates and euglenoids originated in this way from a eukaryotic symbiont: their direct divergence from the ancestral chloroplast cannot be ruled out and indeed has several arguments in its favor. The evidence for and against the view that the chloroplast of the kingdom Chromista was acquired in a single endosymbiotic event is discussed. The possibility that even the chloroplast of Chlorarachnion might have been acquired during the same symbiosis that created the cryptomonad cell, if the symbiont was a primitive alga that had chlorophyll a, b and c as well as phycobilins, is also considered. An alga with such a combination of pigments might have been ancestral to all eukaryote algae.