Debris disks are tenuous, dust-dominated disks commonly observed around stars over a wide range of ages. Those around main sequence stars are analogous to the Solar Systems Kuiper Belt and Zodiacal light. The dust in debris disks is believed to be continuously regenerated, originating primarily with collisions of planetesimals. Observations of debris disks provide insight into the evolution of planetary systems; the composition of dust, comets, and planetesimals outside the Solar System; as well as placing constraints on the orbital architecture and potentially the masses of exoplanets that are not otherwise detectable. This review highlights recent advances in multiwavelength, high-resolution scattered light and thermal imaging that have revealed a complex and intricate diversity of structures in debris disks, and discusses how modeling methods are evolving with the breadth and depth of the available observations. Two rapidly advancing subfields highlighted in this review include observations of atomic and molecular gas around main sequence stars, and variations in emission from debris disks on very short (days to years) timescales, providing evidence of non-steady state collisional evolution particularly in young debris disks.