Liquid crystals are renowned for being the basis of the modern display industry, owing to their unique material properties. They are birefringent, making them manipulable with electric fields and capable of altering light. They are also deformable, yet reconfigurable because they are elastic: their rod-like molecules have an energetic tendency to align with one another. Being ordered materials, they respond to their confining geometry by creating patterned molecular structures and defects - localized, ``melted'' areas of disorder that can lower the energetic distortion in the system. Inclusions within the material that locally disrupt the molecular order are driven to assemble within defects to reduce the system energy. With self-assembly being one of the few realistic ways of templating nanomaterials, the energetics behind defects must be studied for greater control before they can be used to engineer materials for nanotechnology. In this work, I delve into how boundary geometry results in elaborate molecular patterns and defects by designing systems with holes and curvatures to probe elastic mechanisms. My systems are composed of one of either two types of liquid crystals: nematics, where molecules orient along a preferred direction, and cholesterics, where molecules not only align but must additional stack in a helical fashion. In a many-holed system filled with nematics, I exploit the connection between regions of negative Gaussian curvature and specific elastic distortions to stabilize ordered arrays of point defects and remarkable line defects that were previously only seen in more complex liquid crystal phases. With simulations, I uncover the role of certain types of elastic deformations in forming distinct defect structures, and I experimentally switch between these structures through controlled annealing with temperature and electric fields. Then, I investigate a cholesteric confined within a shell, tuning the anchoring at the liquid crystal-water interface with surfactants to change the topology of the system and to examine transitions between different types of cholesteric defects. Lastly, the wetting energy of functionalizable nanoparticles is regulated to direct the particle assembly into patterns dictated by the liquid crystal anchoring at the system interface. The principles of how substrate curvature, topology, and anchoring conditions influence defects and the use of liquid crystal patterning as a self-assembly tool is demonstrated.