Low-dimensional materials have attracted intense interest due to their unconventional properties and promising potential for applications. In this thesis, state-of-art computational methods are employed to study the syntheses, structures, properties, and applications of low-dimensional materials, including carbon nanotube, graphene, boron nitride and transition metal dichalcogenides. Special focus is given to the atomistic mechanism of chemical vapor deposition growth, defect structure and properties, Li-ion battery, and catalytic hydrogen production. Design of novel materials based on Materials Genome approach will also be presented.