The overall architecture of our solar system was established more than 4 billion years ago, through an era of planetary formation lasting tens to perhaps hundreds of millions of years. In this talk, I will discuss current models for the origin of the terrestrial planets in our solar system, which also provide the conceptual framework for understanding the formation of Earth-like planets in extra-solar planetary systems. The final stage of terrestrial planet formation is believed to involve giant collisions between tens to perhaps hundreds of lunar to Mars-sized protoplanets. As protoplanets collide and merge, the number of planets is decreased and the dynamical stability of the system is increased, until finally only a few planets on stable orbits remain. This stochastic process yields a broad range of possible final planetary configurations, even for similar starting conditions. A specific and well-studied event during this era in our solar system was the last giant collision experienced by the Earth, which is believed to have led to the origin of the Moon. Hydrodynamical simulations, together with properties of the Earth-Moon system, can be used to constrain the characteristics of the Moon-forming impact and its substantial effects on our early planet.