The Kepler mission has led to a revolution in the study exoplanet systems. The predictions of theories of planet formation can now be compared to the diverse sample of planetary systems Kepler has discovered. Achieving the most detailed characterizations possible of Kepler's planetary systems is key to realizing the mission's full potential and clearing up theoretical uncertainties. We apply the powerful technique of Markov-chain Monte Carlo to infer planet properties from transit-timing variation measurements. We use these techniques to make precise measurements of the planet masses and orbital parameters of a sample of Kepler multi-planet systems. We will use the detailed information about these planets to address questions about the origins and evolution of these systems. We will explore the long-term stability of the systems that we characterize with numerical integrations along with analytic modeling. This will include exploring the sensitivity of these systems’ stability to changes in planet eccentricities and spacing. Finally we will investigate whether assembly of planetary embryos under the dynamical influence of a gaseous disk can recreate the features of the multi-planet systems we observe. Understanding the origins of these systems will shed light on questions regarding the origin and evolution of our own solar system and how frequently Earth-like planets form around other stars.