At least 20% of nearby main sequence stars are surrounded by disks of dusty material resulting from the collisional erosion of planetesimals, larger bodies similar to asteroids and comets in our own Solar System. The resulting dust can be observed via scattered light at visible to near-infrared wavelengths or thermal emission at mid-infrared to millimeter wavelengths. Since the dust-producing planetesimals are expected to persist in stable regions like belts and resonances, the locations, morphologies, and physical properties of dust in these debris disks provide probes of planet formation and subsequent dynamical evolution. Observations at millimeter wavelengths are especially critical to our understanding of these systems, since the large grains that dominate emission at these long wavelengths do not travel far from their origin and therefore reliably trace the underlying planetesimal distribution. I will present ongoing work that uses observations of the angularly resolved brightness distribution and the spectral dependence of the flux density to constrain both the structure and grain size distribution of nearby debris disks. In particular, I will show new ALMA observations that place constraints on the position, width, surface density gradient, and any asymmetric structure of several well-known debris disks (including the Fomalhaut system). Together these results provide an exciting foundation to investigate the dynamical evolution of planetary systems through multi-wavelength observations of debris disks.