This thesis focuses on the dynamical interaction between the gaseous component of a protoplanetary disk and the solid bodies within. We identify and characterize new dynamical behaviors of solid bodies ranging from micronsize dust grains to Jupiter-size planets, using hydrodynamics simulations accelerated by graphics processing units (GPUs). Chapter 1 outlines the relevant physics and explains our research motivation. Chapter 2 gives a detail description of our GPU hydrodynamics code PenGUIn. Our benchmark shows that, running on a GTX-Titan graphics card, PEnGUIn can update 25 million grid cells per second in a three-dimensional (3D) calculation. Chapter 3 combines PEnGUIn simulations and semi-analytic calculations to demonstrate the existence of a new disk instability, called the irradiation instability. We find that when the star exerts a sufficiently strong radiation pressure, the interplay between dust grains, gas, and radiation is unstable to linear perturbations, and, in extreme cases, can result in “clumping”, local surface density enhancements beyond 10 times the initial value. In Chapter 4 we consider disk gaps opened by giant planets. We determine how the average surface density inside the gap, Sum_gap, depends on planet-to-star mass ratio q, Shakura-Sunyaev viscosity parameter alpha, and disk height-to-radius aspect ratio h=r. We derive an analytical scaling that predicts Sum_gap proportional to q^-2 alpha (h/r)^5, and show that it compares well to results determined numerically with both PEnGUIn and ZEUS90, a modified version of the publicly available code ZEUS. In the end, we turn our attention to Earth-size planets which exchange mass and angular momentum with the disk without significantly modifying the local disk structure. Most work done on this topic has been under the assumption of an infinitely thin 2D disk, and so a precise description in 3D has been lacking. 3D simulations with PEnGUIn described in Chapter 5 reveal that vertical motion plays an important role in the 3D flow field around an embedded planet, and has a direct impact on both planet accretion and migration. In particular, the size of the planet’s atmosphere is much smaller than anticipated, and the corotation torque on the planet deviates significantly from 2D predictions.