In contrast to the canonical planets of our solar system, with semimajor axes in the familiar range of ~ 0.3���30 au, exoplanets have been detected at considerably shorter and longer distances from their host stars. These planets, at the innermost and outermost reaches of planetary systems, have challenged many hitherto foundational ideas of planetary formation and evolution that were based solely on knowledge of our own solar system. This thesis addresses some of the emergent puzzles posed by the orbital and interior dynamics of planets orbiting very close and far away from their stars. Chapters II-III consider the origins of planets on very short-period orbits. Two and a half decades ago, the discovery of the first hot Jupiter marked the dawn of exoplanet detections around sunlike stars. The existence of these extremely irradiated Jovian planets (orbital periods ��� 5 days) runs in stark contrast to the utter absence of material orbiting interior to Mercury in our own solar system. This striking discrepancy between the close-in planetary content of observed systems and our own ��� together with the notion that, interior to the "snow lines" of stars at stello-centric radii of several au, water ice is not available to contribute to the accretion of the several Earth-mass cores necessary for runaway core accretion ��� has led to many works aiming to explain how Jovian-mass (��� 0.1MJ) planets can migrate inward to become hot Jupiters after forming beyond the snow lines of their stars. One such migration mechanism, known as high-eccentricity migration, occurs when a Jovian planet is excited to extremely high eccentricity such that it experiences significant tidal dissipation at perihelion passage, promoting orbital decay to a short-period orbit. For cases such as the massive (~ 9MJ), eccentric (e ~ 0.5) hot Jupiter HAT-P-2b ��� for which the exterior perturber is characterized ��� the eccentric orbital state encodes information about the tidal history of the planet. In Chapter II, I outline a method for constraining the tidal dissipation rate in eccentric hot Jupiters such as HAT-P-2b and its analogues. In Chapter III, I consider the opposite limit of possibilities: local conglomeration. While observations of highly eccentric, tidally unstable hot Jupiters imply some hot Jupiters must form through high-eccentricity migration, I present a -2/7 power law prediction which naturally follows from a basic picture of viscous accretion and inner magnetic truncation of protoplanetary disks. This power law, combined with simple tidal corrections, agrees well with the observed period-mass distribution of hot Jupiters, possibly lending new credence to the hypothesis that hot Jupiters predominantly form in situ, near their observed close-in positions. Next, with Chapter IV, we move on from the inner regions of planetary systems to address the interior dynamics of our furthest observed solar system planets, Uranus and Neptune. The so-called "ice giants" present a major challenge to interior modeling efforts due not only to a relative lack of spacecraft coverage compared to other solar system planets, but also because of a compositional degeneracy which inherently arises from their intermediate densities. An especially confounding issue surrounding these planets has been the extremely low heat flux of Uranus compared to Neptune. Chapter IV addresses these challenges with the application of novel thermodynamic constraints that follow in the case where hydrogen and water are taken to be immiscible major constituents. As discussed in Chapter IV, this model framework can satisfy the observed masses, radii, and gravitational harmonics of these planets ��� without being at odds with observations of the magnetic fields. Importantly, as Chapter IV shows, hydrogen-water immiscibility in the deep interiors of Uranus and Neptune can offer a natural explanation for the disparate heat fluxes ��� but characteristically similar magnetic fields ��� of Uranus and Neptune. Following this discussion of the outermost directly observed planets in our solar system, Chapters V-VI delve into the orbital dynamics of planets on extremely wide (hundred-au) orbits, with a specific emphasis on the hypothesized Planet Nine. In our own solar system, the existence of a massive planet on such a wide orbit, with considerable eccentricity (e ��� 0.1) and inclination (i ~ 20��), has been proposed to explain several dynamical features of the outer solar system. In Chapter V, I describe how this very distant planet could affect the dynamics down to the innermost reaches of the solar system, through secular modulation of the so-called "invariable" plane of the canonical planets, relative to the solar spin axis. Next, in Chapter VI, I numerically derive a prior distribution for the relative occupation of individual mean-motion resonances with this planet by eccentric small bodies, showing that assumption of low-order resonances with observed objects is not a viable means to determine the current true anomaly of Planet Nine. Finally, in Chapter VII, concluding remarks are given, and the findings of this work are discussed in relation to the ongoing exploration of related topics in planetary system dynamics.