Several properties of the Solar System, including the wide radial spacing of the giant planets, can be explained if planets radially migrated by exchanging orbital energy and momentum with outer disk planetesimals. Neptune's planetesimal-driven migration, in particular, has a strong advocate in the dynamical structure of the Kuiper belt. A dynamical instability is thought to have occurred during the early stages with Jupiter having close encounters with a Neptune-class planet. As a result of the encounters, Jupiter acquired its current orbital eccentricity and jumped inward by a fraction of an astronomical unit, as required for the survival of the terrestrial planets and from asteroid belt constraints. Planetary encounters also contributed to capture of Jupiter Trojans and irregular satellites of the giant planets. Here we discuss the dynamical evolution of the early Solar System with an eye to determining how models of planetary migration/instability can be constrained from its present architecture. Specifically, we review arguments suggesting that the Solar System may have originally contained a third ice giant on a resonant orbit between Saturn and Uranus. This hypothesized planet was presumably ejected into interstellar space during the instability. The Kuiper belt kernel and other dynamical structures in the trans-Neptunian region may provide evidence for the ejected planet. We favor the early version of the instability where Neptune migrated into the outer planetesimal disk within a few tens of millions of years after the dispersal of the protosolar nebula. If so, the planetary migration/instability was not the cause of the Late Heavy Bombardment. Mercury's orbit may have been excited during the instability.