The large number of observed exoplanets (700) provides important constraints on their origin as deduced from the mass-period diagram of planets. The most surprising features in the diagram are (1) the (apparent) pileup of gas giants at a period of ~500 days (~1?AU) and (2) the so-called mass-period relation, which indicates that planetary mass is an increasing function of orbital period. We construct the evolutionary tracks of growing planets at planet traps in evolving protoplanetary disks and show that they provide a good physical understanding of how these observational properties arise. The fundamental feature of our model is that inhomogeneities in protoplanetary disks give rise to multiple (up to 3) trapping sites for rapid (type?I) planetary migration of planetary cores. The viscous evolution of disks results in the slow radial movement of the traps and their cores from large to small orbital periods. In our model, the slow inward motion of planet traps is coupled with the standard core accretion scenario for planetary growth. As planets grow, type?II migration takes over. Planet growth and radial movement are ultimately stalled by the dispersal of gas disks via photoevaporation. Our model makes a number of important predictions: that distinct sub-populations of planets that reflect the properties of planet traps where they have grown result in the mass-period relation, that the presence of these sub-populations naturally explains a pileup of planets at ~1?AU, and that evolutionary tracks from the ice line do put planets at short periods and fill an earlier claimed "planet desert"—a sparse population of planets in the mass-semimajor axis diagram.
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