Recent findings are summarized in support of the view that mitochondria (including hydrogenosomes) and plastids (including complex ones) descend from symbiotic associations of once free-living organisms. The reasoning behind endosymbiotic hypotheses stems from a comparison of biochemistry and physiology in organelles with that in free-living cells; their strength is shown to lie in the specific testable predictions they generate about expected similarity patterns among genes. Although disdained for many decades, endosymbiotic hypotheses have gradually become very popular. In the wake of that popularity, endosymbiotic hypotheses have been formulated to explain the origins of eukaryotic cell compartments and structures that have no biochemical similarity to free-living cells. In particular, it has become fashionable in recent years to entertain the century-old notion that the nucleus might also descend from an endosymbiotic bacterium. A critique of that hypothesis is formulated and a simple alternative to it is outlined, which derives the nuclear compartment in a mitochondrion-bearing cell.