Approximately 90 Earth-crossing asteroids had been discovered through September 1989. Discovery is thought to be complete at absolute V magnitude (H) = 13.2 (the magnitude of the brightest known object, diameter ∼8.1 km), and about 6 percent complete at H = 17.7 (typical diameter about 1 km). The calculated mean probability of collision of Earth-crossing asteroids with Earth is (4.2 ± 1.7) × 10⁻⁹ yr⁻¹. When multiplied by the estimated population of 1030 ± 470 at H = 17.7, this probability yields a collision rate of (4.3 ± 2.6) × 10⁻⁶ yr⁻¹ for asteroids larger than about 1 km in diameter. At H = 15.8, roughly equivalent to asteroid diameters more than 2 km, the estimated collision rate is ≈7 × 10⁻⁷ yr⁻¹, and at 8-km diameter, the rate is ≈3 × 10⁻⁹ yr⁻¹. Comet nuclei with diameters more than 2.5 km are estimated to strike the Earth at the rate of ≈ 10⁻⁷ yr⁻¹; comets larger than 10 km in diameter probably strike at a rate ≈10⁻⁸ yr⁻¹. Impact of asteroids probably dominates the production of craters smaller than 30 km in diameter, whereas comet impact probably forms most craters larger than 50 km. The production rate for craters larger than 20 km in diameter, estimated from the astronomical evidence, is (4.9 ± 2.9) × 10⁻¹⁵ km⁻² yr⁻¹; this rate is consistent with the cratering rate estimated by Grieve from the geologic record for the last 120 m.y.