This Thesis discusses nonadditive mixing, which occurs when the volume of a mixed state is either smaller (negative) or larger (positive) than the sum of the volumes of its individual components. However, in the context of colloidal and nanoparticle (NP) mixtures, instances of non-additivity are rare, and systematic studies of such mixtures are non-existent. This thesis focuses on investigating nanoparticle non-additive mixing behavior by manipulating the interactions of DNA-chains grafted to them and nanoparticle cores with either non-convex or convex shapes.The first part of the thesis examines systems containing polyhedra as a baseline and maps their phase diagrams to control negative-mixing behavior. By increasing the extent of shape concavity, the study demonstrates that nonadditivity is associated with athermal crystallization of binary mixtures into nanocrystal superlattices. In the second part, the focus is on spherical particles designed to represent highly coarse-grained descriptions of DNA-grafted patchy nanoparticles which are able to exhibit positive-mixing behavior. By varying the patch-patch angle and the degree of non-additivity, a diverse range of phase behaviors is observed in mixtures of two-patch particles and fully grafted spherical particles. These behaviors result in morphologies such as the gyroid, cylinder, honeycomb, and two-layered crystal structures. The findings also reveal that both a minimum positive nonadditivity and multivalence of interactions are necessary for the formation of ordered network mesophases in the systems studied. The last study examines mixtures of four-patch nanoparticles with patches arranged with a tetrahedral symmetry to explore how positive non-additivity affects the system’s self-assembly behavior into a crystalline phase with a diamond lattice structure. Our simulation results indicate that higher non-additivity has a minimal effect on phase behavior but enhances the kinetics of the formation of the diamond phase. Overall, the text explores non-additive mixing behavior in colloidal and nanoparticle mixtures by manipulating the energetic interactions of the nanoparticle coronas (representing DNA-mediated inter-species selectivity), and the entropy packing interactions of the nanoparticle cores with different shapes. The findings shed light on the relationship between anisotropic interparticle interactions and phase behavior, highlighting the importance of non-additivity and multivalence in the formation of ordered binary compound crystals and network mesophases.