Laboratory and in situ measurements show that scattering properties of natural nonspherical particles can be significantly different from those of volume-or surface-equivalent spheres, thus suggesting that Mie theory may not be suitable for interpreting satellite reflectance measurements for dustlike tropospheric aerosols. In this paper we use the rigorous T-matrix method to extensively compute light scattering by shape distributions of polydisperse, randomly oriented spheroids with refractive indices and size distributions representative of naturally occurring dust aerosols. Our calculations show that even after size and orientation averaging, a single spheroidal shape always produces a unique, shape-specific phase function distinctly different from those produced by other spheroidal shapes. However, phase functions averaged over a wide aspect-ratio distribution of prolate and oblate spheroids are smooth, featureless, and nearly flat at side-scattering angles and closely resemble those measured for natural soil and dust particles. Thus, although natural dust particles are, of course, not perfect spheroids, they are always mixtures of highly variable shapes, and their phase function can be adequately modeled using a wide aspect-ratio distribution of prolate and oblate spheroidal grains. Our comparisons of nonspherical versus projected-area-equivalent spherical particles show that spherical-nonspherical differences in the scattering phase function can be large and therefore can cause significant errors in the retrieved aerosol optical thickness if Mie theory is used to analyze reflectance measurements of nonspherical aerosols. On the other hand, the differences in the total optical cross sections, single-scattering albedo, asymmetry parameter of the phase function, and backscattered fraction are much smaller and in most cases do not exceed 10%. This may suggest that for a given aerosol optical thickness the influence of particle shape on the aerosol radiative forcing is negligibly small. Spherical-nonspherical differences in the extinction-to-backscatter ratio are very large and should be explicitly taken into account in inverting lidar measurements of dustlike aerosols.