It was once widely believed that planets formed peacefully in situ in their proto-planetary disks and subsequently remain in place. Instead, growing evidence suggests that many giant planets undergo dynamical rearrangement that results in planets migrating inward in the disk, far from their birthplaces. However, it remains debated whether this migration is caused by smooth planet-disk interactions or violent multi-body interactions. Both classes of model can produce Jupiter-mass planets orbiting within 0.1 AU of their host stars, also known as hot Jupiters. In the latter class of model, another planet or star in the system perturbs the Jupiter onto a highly eccentric orbit, which tidal dissipation subsequently shrinks and circularizes during close passages to the star. We assess the prevalence of smooth vs. violent migration through two studies. First, motivated by the predictions of Socrates et al. (2012), we search for super-eccentric hot Jupiter progenitors by using the "photoeccentric effect" to measure the eccentricities of Kepler giant planet candidates from their transit light curves. We find a significant lack of super-eccentric proto-hot Jupiters compared to the number expected, allowing us to place an upper limit on the fraction of hot Jupiters created by stellar binaries. Second, if both planet-disk and multi-body interactions commonly cause giant planet migration, physical properties of the proto-planetary environment may determine which is triggered. We identify three trends in which giant planets orbiting metal rich stars show signatures of planet-planet interactions: (1) gas giants orbiting within 1 AU of metal-rich stars have a range of eccentricities, whereas those orbiting metal-poor stars are restricted to lower eccentricities; (2) metal-rich stars host most eccentric proto-hot Jupiters undergoing tidal circularization; and (3) the pile-up of short-period giant planets, missing in the Kepler sample, is a feature of metal-rich stars and is largely recovered for giants orbiting metal-rich Kepler host stars. These two studies suggest that both disk migration and planet-planet interactions may be widespread, with the latter occurring primarily in metal-rich planetary systems where multiple giant planets can form. Funded by NSF-GRFP DGE-1144152.