In this talk I will first review the concepts of the curvature and torsion in the Riemannian-Cartan (RC) geometry. By imposing the teleparallelism, the theory of teleparallel equivalent to general relativity (TEGR) with the Lagrangian T can be constructed in the Weitzenbock geometry. Then some problems with torsion will be discussed briefly. After the introduction, I will review some applications in the cosmology, such as f(T) and teleparallel dark energy models. Finally, I will discuss my recent work of the conformally invariant models induced by Kaluza-Klein reduction in Teleparallelism.