Modified teleparallel gravity

I will review the basic construction of teleparallel gravity and its modifications, with a special emphasis on local Lorentz transformations in the tetrad space. One of these modified models, the f(T), is widely used for cosmological model building. I will explain how (linear) cosmological perturbations should be treated in f(T) and in similar models. Finally I will discuss the problem of dynamical structure and Hamiltonian analysis for modified teleparallel gravity.