The search for planets around other suns is one of the most daunting tasks astronomers have tackled; here two astronomers sum up the progress to date. Mammana (Fleet Space Theater, San Diego) and McCarthy (Univ. of Arizona) build their discussion around a brief history of their discipline, beginning with the Greek philosophers, who accepted the plurality of worlds as a given. With the gradual improvement of modern astronomical instruments, the true magnitude of the universe became known and the question became not whether there were planets around other stars, but when someone would detect one. In 1963, Peter Van de Kamp of Swarthmore was the first to claim identification of an extrasolar planet, based on three decades of measurements of the position of Barnard's Star. Fellow astronomers failed to duplicate his data, but there were plenty of others on the trail. McCarthy announced his own discovery in 1984: a companion to an extremely faint star known as VB8. Debate raged over whether the companion was a planet like Jupiter or a so-called ""brown dwarf""--an object just below stellar size but with orders of magnitude larger than any known planet. Disks of diffuse material, of the sort from which planetary systems are believed to form, have been detected around a number of stars. The Hubble Space Telescope and a new generation of ground-based scopes have pushed the observational frontiers farther out; and several astronomers are lobbying for even larger instruments, based either in space or on the moon, where observing conditions will be far better than on Earth. A new wave of discoveries--too recent for the authors to address them--seems to have made a firm case for the existence of planets around at least two other stars. A somewhat dry but workmanlike survey of its subject, with interesting sidelights on astronomers and their equipment.