It is known that large asteroids and comets can collide with the Earth with severe consequences. Although the chances of a collision in a person's lifetime are small, collisions are a random process and could occur at any time. This book, which was first published in 2004, collects the latest thoughts and ideas of scientists concerned with mitigating the threat of hazardous asteroids and comets. It reviews knowledge of the population of potential colliders, including their numbers, locations, orbits, and how warning times might be improved. The structural properties and composition of their interiors and surfaces are reviewed, and their orbital response to the application of pulses of energy is discussed. Difficulties of operating in space near, or on the surface of, very low mass objects are examined. The book concludes with a discussion of the problems faced in communicating the nature of the impact hazard to the public.