Immense insight into fundamental processes necessity for the fabrication of nanostructures is gathered from studying the self-assembly of colloidal suspensions. These fundamental processes include crystal nucleation and particle aggregation. In this thesis, we developed an efficient computational framework to study the self-assembly of same-sized, spherical colloids with intermolecular interactions, such as the programmable DNA-mediated interaction. In the first part of this thesis, we studied the interfacial dynamics during colloidal crystallization. The interfacial dynamics of binary crystals was probed by weak impurity segregated growth. This segregated growth was interpreted as the number of surface bonds required to crystallize a fluid particle. For short-ranged DNA-mediated interactions, an integer number of surface bonds are needed for a particle to crystallize, which was verified by experiments. This demonstrates the utility of our computational framework to replicate growth kinetics of DNA-directed particle self-assembly. In the second part of this thesis, we studied the kinetic control of crystal structure in DNA-directed self-assembly. For a dilute colloidal suspension, with weak intermolecular interaction between similar particles, binary crystals can assemble into close-packed (cp) or body-centered-cubic (bcc) structures based on thermodynamic or kinetic factors. Under fast kinetic conditions bcc crystals assemble from the suspension. For the same intermolecular interactions and slow kinetic conditions, cp crystals are observed within the suspension.