Topological insulator (TI) has attracted more and more attention from physicists, due to its peculiar electronic properties; for instance, topologically protected surface state, spin-momentum locking etc. This book covers the works in my whole PhD. project, which includes the researches on the Bi2Se3-family topological insulators (TIs) with different defects (lattice mismatch, magnetic and non-magnetic doping atoms) and the study of the proximity effect of TI to graphene layer with the focus on spin properties. Research works in this project could provide a guideline to the experimentlists and a fundamental explanation to other theorists, who work on the electronic properties of TI and its related heterostructure in the field of spintronic science.