Hot Jupiters (giant planets with orbital periods less than 10 days) and warm Jupiters (giant planets with orbital periods between 10-300 days) are major topics in exoplanetary dynamics, with unresolved puzzles regarding their dynamical histories and migration. Many observed systems show hints of a dynamically-active past, such as large stellar spin-orbit misalignments (obliquities) in hot Jupiter systems, and substantial eccentricities in warm Jupiter systems. Some stellar binaries present similar puzzles as close-in exoplanets, including a range of eccentricities and obliquities. This dissertation explores the spin and orbital evolution of close-in giant exoplanets and binaries due to the presence of an external companion. A third body may perturb the orbit of the planet or binary, leading to secular changes in eccentricity and inclination. Alongside the secular evolution of the orbit, an oblate star experiences a torque from the planet or binary companion, leading to precession of the spin axis and obliquity evolution. This dissertation explores such spin-orbit dynamics in a variety of contexts: (1) I conduct a population synthesis of hot Jupiter migration in stellar binaries due to Lidov-Kozai cycles, and present the resulting distributions of spin-orbit misalignment angles and formation efficiencies. (2) Considering both hot and warm Jupiter systems with external planetary companions, I identify the requirements for the outer planet to generate dramatic obliquity growth through a secular spin-orbit resonance, which may be encountered as the host star spins down due to magnetic braking. (3) I consider stellar binaries with a tertiary companion, and identify the system architectures in which the tertiary may affect the obliquities of the inner binary members. (4) I consider how an inclined circumbinary disk may excite obliquities in stellar binaries. In addition to spin-orbit dynamics, this dissertation also explores two different mechanisms for exciting eccentricities in warm Jupiter systems, due to secular perturbations from inclined companions, and in-situ scattering.