This paper reviews coagulation models for planet formation in the Kuiper Belt, emphasizing links to recent observations of our and other solar systems. At heliocentric distances of 35-50 AU, single annulus and multiannulus planetesimal accretion calculations produce several 1000 km or larger planets and many 50-500 km objects on timescales of 10-30 Myr in a Minimum Mass Solar Nebula. Planets form more rapidly in more massive nebulae. All models yield two power law cumulative size distributions, N_C propto r^{-q} with q = 3.0-3.5 for radii larger than 10 km and N_C propto r^{-2.5} for radii less than 1 km. These size distributions are consistent with observations of Kuiper Belt objects acquired during the past decade. Once large objects form at 35-50 AU, gravitational stirring leads to a collisional cascade where 0.1-10 km objects are ground to dust. The collisional cascade removes 80% to 90% of the initial mass in the nebula in roughly 1 Gyr. This dust production rate is comparable to rates inferred for alpha Lyr, beta Pic, and other extrasolar debris disk systems.

invited review for PASP, March 2002. 33 pages of text and 12 figures