Optical matter assemblies, specifically nanoparticles that interact and are electrodynamically bound into ordered structures, represent a new type of material that has novel structural and dynamic properties that are of fundamental and practical interest. Polarizable (and/or plasmonic) nano-particles exhibit strong interactions in optical fields (e.g., in optical traps) that result in emergent structures and non-equilibrium phenomena such as non-reciprocal forces and negative torques. Although these effects have been predicted and have begun to be demonstrated experimentally, our understanding of these phenomena is still limited. In this dissertation I will discuss findings concerning the properties of optical matter systems. I will show that the long-range and periodic interactions between particles in optical matter systems that are the result of the coherent light scattered by the particles in the system have important electrodynamic and structural consequences. Symmetry also plays an important role in the dynamics of optical matter systems, and I will show that broken symmetry of several different types results in non-conservative dynamics. I will also show that rearrangements in optical matter systems are similar to reactions in chemical systems.