A combination of density functional theory and a tight-binding model offers a robust means to describe the structure, vibrations, and electronic states of silicene. In this chapter we give an overview of the electronic structure and phonon dispersions of silicene and its fully hydrogenated derivative, silicane. We discuss the dynamical stability of the buckled silicene and silicane lattices and we present their phonon dispersions. We discuss the first-principles electronic band structure of ideal, free-standing silicene, paying particular attention to the small band gap opened by spin–orbit coupling, which renders the material a topological insulator. We look at the tight-binding description of silicene and examine the effects of an external electric field which, above a critical electric field, counters the spin–orbit gap and triggers a phase transition into a band-insulator state in which the band gap is linearly tunable by the electric field. We also present the tight-binding description of silicane which, parameterised by density functional theory, sheds light on the importance of long-range hopping in this material.