In this Review, I discuss recent developments on the long-term dynamical evolution of exoplanet systems, focusing on how distinctive dynamical processes may have shaped the orbital architectures of observed populations. I include three applications that highlight part of my own work. First, I examine the high-eccentricity tidal migration of hot Jupiters from a phase of dynamical instability and subsequent secular interactions in two-planet systems. Second, secular chaos as the origin of ultra-short-period planets with extreme period ratios. Third, secular resonance sweeping driven by a dispersing protoplanetary disk as the origin hot Neptunes residing in polar orbits. Finally, I discuss how upcoming observations will allow further constraining the prevalence of these dynamical processes.

Systems near mean-motion resonances (MMRs) are subject to large transit-timing variations (TTVs). The amplitude and period of the TTVs strongly depend on the distance to exact MMR and the planetary eccentricities which are shaped during the formation and long-term evolution of the system. For close-in planets, the tides raised by the star provide a source of dissipation, placing the planets further away from the MMR. In this work, we will discuss how the tidal interactions with the central star play an important role in shaping the period ratios and resonant angles in resonant chains. Moreover, we will show how they can impact the TTVs and therefore how the TTVs could serve as a means to put constraints on the tidal history of planetary systems. The study will focus on the four-planet resonant chain of Kepler-80.

The Nearby Young Moving Groups sample the critical age when primordial disks around stars complete their transformation into planetary systems with associated debris. Millimeter wavelengths provide direct access to cool material in these circumstellar disks. The high angular resolution of interferometry at these long wavelengths enables resolved observations of solids in an optically thin regime, as well as the thermal, chemical, and dynamical structure of gas, if present. In this contribution, I briefly review the evolving landscape of millimeter telescopes, with emphasis on the revolutionary capabilities of the new international Atacama Large Millimeter/submillimeter Array (ALMA) and describe pertinent early science results.

This work considers debris disks whose spectra can be modelled by dust emission at two different temperatures. These disks are typically assumed to be a sign of multiple belts, but only a few cases have been confirmed via high resolution observations. We derive the properties of a sample of two-temperature disks, and explore whether this emission can arise from dust in a single narrow belt. While some two-temperature disks arise from single belts, it is probable that most have multiple spatial components. These disks are plausibly similar to the outer Solar System's configuration of Asteroid and Edgeworth-Kuiper belts separated by giant planets. Alternatively, the inner component could arise from inward scattering of material from the outer belt, again due to intervening planets. For either scenario, the ratio of warm/cool component temperatures is indicative of the scale of outer planetary systems, which typically span a factor of about ten in radius.

Using N-body simulations with planet-disk interactions, we present a mechanism capable of forming compact systems of hot super Earths such as Kepler 11. Recent studies show that outward migration is common in the inner parts of radiative disks. However we show that two processes naturally tip the balance in favor of inward migration. First the corotation torque is too weak to generate outward migration for planetary embryos less massive than 4M⊕. Second, system of multiple embryos generate sustained non-zero eccentricities that damp the corotation torque and again favor inward migration. Migration and accretion of planetary embryos in realistic disks naturally produce super Earths in resonant chains near the disk inner edge. Their compact configuration is similar to the observed systems.