Recent advances in radial velocity and transit surveys have led to a large increase in the number of detected multi-planet systems, indicating that such systems are common in the Galaxy. These multi-planet systems bear little resemblance to our own Solar System: most of the detected exo-planets are Super-Earths or Mini-Neptunes, and have periods shorter than 200 days. The discovery of these systems have challenged conventional notions of planetary dynamics, and exposed fertile areas of research. In this thesis, I present three papers on the dynamical evolution of multi-planet systems in the context of findings by Kepler and similar missions. (1) I study the dynamical effects of eccentric and/or misaligned external companions on inner multi-planet systems. (2) I study the effect of hard scatterings between outer giant planets on inner multi-planet systems, and derive a mathematical model to compute the distribution of the final system parameters. (3) Turning my attention inward, I propose a low-eccentricity migration mechanism to explain the origins of ultra-short-period planets, an unusual subset of Kepler planets whose origins are presently not well understood.