Light-matter interactions have been a subject of fascination for many years. One of the ways to examine the interactions of matter on the micro or nano scale with light is to use optical tweezers or optical trapping. When two or more micron- or nano-sized particles are illuminated by an optical trap, their mutual scattering of light results in active, non-equilibrium and self-organizing ordered structures known as optical matter. This phenomenon is known as optical binding. Optical binding between pairs of metallic nanoparticles such as silver (Ag NPs) and gold (Au NPs), which manifest a strong plasmonic electric dipole (ED) resonance, have been explored extensively in the past. However, experimental studies of optical binding interactions between a pair of high-index dielectric nanoparticles have not been previously reported. As will be shown in this thesis, due to their high index of refraction, silicon nanoparticles (Si NPs) exhibit a significant optical magnetic dipole (MD) resonance at vis/IR frequencies. We show in this thesis the new experimental phenomenon of magnetic optical binding in pairs of Si NPs. The pairwise interactions between nanoparticles in optical matter systems lead to interesting dynamics including non-reciprocal (i.e., unequal and opposite) effects and the emergence of new forces associated with them. These effects have been studied in the context of Ag NP heterodimers where the broken symmetry due to their dissimilar sizes leads to non-reciprocity in the system. However, experimental studies of non-reciprocal forces in high-index dielectric nanoparticle heterodimers have not been previously reported. In this thesis, we provide experimental evidence of optical magnetic binding induced non-reciprocal forces in pairs of Si NP heterodimers. We also show that the behavior of the non-reciprocal forces in Si NP heterodimers is different from that observed in Ag NP heterodimers. We extend our study of optical matter from just pairwise interactions between two nanoparticles to arrays of more than two nanoparticles. The many-body interactions that arise from such systems are of great interest. We present a new way to break symmetry and generate non-reciprocal forces in a system of optically bound Ag NP nanoparticles through many-body electrodynamic coupling. We show that the non-reciprocal forces are many-body in nature and only arise for three or more particles maintained in a bent configuration where the OM system is not spatially symmetric. The requisite symmetry breaking is realized in experiment by trapping many Ag nanoparticles using an optical ring trap to sustain the bent configuration. We also explore the collective scattering of many-body optical matter systems. This is done by using the theory of collective modes formulated earlier in the context of Ag NPs. We extend the investigation of collective modes to many-body optical matter systems consisting of Si NPs. We show that there are significant differences between the many-body behavior in Ag NP and Si NP optical matter systems. The advantage of the collective mode approach is that it helps us reduce the complicated many-body nature of the scattering of light by multiple nanoparticles to a few dominant collective scattering modes.