The concept of aperoi kosmoi (multiplicity or plenitude of worlds) has had at least four meanings at various times, two capable of yielding images and two not. We explore here the several meanings and their connections with modern astronomical ideas, focusing finally on the one in the minds of the organizers of the present conference. There seem to be at least two dozen ways of potentially detecting or limiting the incidence of “other worlds,” in the sense of potentially habitable planets orbiting other stars, a handful of which have led to detections, false alarms, or both. © 2004 American Institute of Physics