All naturally occurring and most man-made solid particles are nonspherical. Examples include air-pollutants in the nano- to micro-meter range as well as blood constituents, drug particles, and industrial fluid-particle streams. Focusing on the modeling and simulation of inhaled aerosols, theories for both spherical and nonspherical particles are reviewed to analyze the contrasting transport and deposition phenomena of spheres and equivalent spheres versus ellipsoids and fibers.