Models of planet formation are built on underlying physical processes. In order to make sense of the origin of the planets we must first understand the origin of their building blocks. This review comes in two parts. The first part presents a detailed description of six key mechanisms of planet formation: 1) The structure and evolution of protoplanetary disks 2) The formation of planetesimals 3) Accretion of protoplanets 4) Orbital migration of growing planets 5) Gas accretion and giant planet migration 6) Resonance trapping during planet migration. While this is not a comprehensive list, it includes processes for which our understanding has changed in recent years or for which key uncertainties remain. The second part of this review shows how global models are built out of planet formation processes. We present global models to explain different populations of known planetary systems, including close-in small/low-mass planets (i.e., super-Earths), giant exoplanets, and the Solar Systems planets. We discuss the different sources of water on rocky exoplanets, and use cosmochemical measurements to constrain the origin of Earths water. We point out the successes and failings of different models and how they may be falsified. Finally, we lay out a path for the future trajectory of planet formation studies.
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