Simply by nature of their scale and complexity, astrophysical systems are almost always studied by simplifications and effective, parameterized models. Yet even after this considerable simplification, the resulting systems can still host unusual and exciting phenomena. In this dissertation, I study and characterize analytically and numerically many of these behaviors in few-body systems consisting of planets, stars, and black holes (BHs). My work falls into three broad categories: (i) I carry out a comprehensive theoretical analysis of the spin dynamics of planets by studying the "Colombo's Top" system (a rotating planet whose spin axis precesses around its orbital axis, which itself varies in time). In the course of this analysis, I examine: the dynamics of planetary obliquities when surrounded by a dissipating protoplanetary disk, and the capture probabilities of planetary spins into high-obliquity, stable equilibria due to tidal dissipation in two and many-planet systems. I apply these results to assess the spin dynamics and evolution of planets in various, observationally-relevant architectures, such as super Earths with nearby or distant companions. My work is the first to describe comprehensively the complex resonance capture process responsible for the excitation of large obliquities in both integrable, two-planet systems and chaotic, three-planet systems. My results show that super Earths around solar-type stars have a significant chance of capture into various stable high obliquity states; this will have a large impact on their surface/atmosphere conditions. (ii) I use detailed hydrodynamical simulations to understand the nonlinear internal gravity wave breaking process that is responsible for tidal dissipation in white dwarf and early-type stellar binaries. I then use my results to understand the circularization of highly eccentric, massive stellar binaries and to calculate the observational effects of tidal heating in compact white dwarf binaries. (iii) I study the observational signatures of the tertiary-induced merger channel for merging BH binaries, in which a distant companion drives the BH binary into a high-eccentricity orbit via the von Zeipel-Lidov-Kozai mechanism, and the binary then merges due to gravitational wave emission. I study both the spin dynamics of the merging BHs when the tertiary is circular as well as the mass ratio distribution when the tertiary is eccentric, with observational comparisons to the BH mergers seen by the LIGO/VIRGO Collaboration.