The evolutionary processes underlying the differentness of prokaryotic and eukaryotic cells and the origin of the latter's organelles are still poorly understood. For about 100 years, the principle of endosymbiosis has figured into thoughts as to how these processes might have occurred. A number of models that have been discussed in the literature and that are designed to explain this difference are summarized. The evolutionary histories of the enzymes of anaerobic energy metabolism (oxygen-independent ATP synthesis) in the three basic types of heterotrophic eukaryotes those that lack organelles of ATP synthesis, those that possess mitochondria and those that possess hydrogenosomes--play an important role in this issue. Traditional endosymbiotic models generally do not address the origin of the heterotrophic lifestyle and anaerobic energy metabolism in eukaryotes. Rather they take it as a given, a direct inheritance from the host that acquired mitochondria. Traditional models are contrasted to an alternative endosymbiotic model (the hydrogen hypothesis), which addresses the origin of heterotrophy and the origin of compartmentalized energy metabolism in eukaryotes.