The recent impact of Comet Shoemaker-Levy on Jupiter made the world aware of the potential for another worldwide disaster of the sort that purportedly killed off the dinosaurs; here an astronomer assesses the risks. Steel, an Australian research astronomer (Univ. of Adelaide), begins his book with a sober and mathematics-laden discussion of the astronomical probabilities of a major asteroid or comet impacting the Earth, and the probable results--namely, the end of civilization. Nobody who has kept abreast of the scientific research is likely to disagree with this part of his thesis, yet he presents this conclusion dryly and with little concession to the sensibilities of the general reader. Only around chapter five, where he looks into the historical debate about meteor impacts on Earth, does the momentum of his argument begin to mount; unfortunately, many readers will have given up by then, in many cases those who might most enjoy the subsequent chapters, which include a discussion of the possible relation of Stonehenge and the Egyptian pyramids to meteoric bombardments. Steel calculates that dying as the result of a cosmic collision is about twice as likely as dying in an airplane crash, a sobering estimate (especially to those who fear flying). He suggests that the most useful response to the danger is Project Spaceguard, a program combining astronomical resources with the technology of the ``Star Wars'' SDI defense system to detect incoming asteroids and to deflect them with atomic explosions. (Inexplicably, he neglects to mention the perhaps equally significant step of removing a portion of the human population from the target area by colonizing habitats other than Earth.) An important evaluation of one of the key long-range threats to human survival, aimed at a popular audience but full of solid scientific data.