Protoplanetary disks are disks of gas and dust orbiting young stars which form planetary systems. This thesis is devoted to understanding how gravitational interactions in different astrophysical situations effect the structure and dynamical evolution of protoplanetary disks, shaping the planetary systems the disks give birth to. Chapter 2 shows how disk warping in a hydrodynamical disk torqued by a spinning central star and inclined binary companion affects the disk's structure and drives its long-term evolution. Chapter 3 looks at how photoevaporation and the formation of a massive, short-period planet modifies the excitation between the spin-axis of a spinning oblate star and angular momentum axis of a protoplanetary disk generated by the gravitational torque from an inclined binary companion. Chapter 4 derives the conditions a protoplanetary disk must satisfy to undergo the Lidov-Kozai instability, where the disk's eccentricity grows from the gravitational torque exerted on the disk by an inclined binary companion. Chapter 5 derives the conditions a protoplanetary disk around an eccentric binary must satisfy to evolve into an orientation perpendicular to the binary's orbital plane (polar alignment). Chapter 6 shows an extended circumplanetary disk can remain stably tilted out of the planet's orbital plane, provided the torques from the oblate planet and disk self-gravity are sufficiently strong to resist the tidal torque from the planet's host star. The appendix derives a useful dispersion relation for density waves in a viscous, non-Keplerian disk.