Degrees of freedom and local Lorentz invariance in f(T) gravity

f(T) gravity is a generalization of the teleparallel equivalent of general relativity (TEGR), where T is the torsion scalar made up of the Weitzenbock connection. This connection describes a spacetime with zero curvature but with nonvanishing torsion, which fully encodes the gravitational phenomena. We will present recent results in f(T) gravity related with the issue of the degrees of freedom of the theory. In particular, we discuss the recent finding that f(T) gravity has one extra degree of freedom compared with TEGR, which was concluded through a detailed Hamiltonian analysis of the constraint structure of the theory. The physical interpretation of this result at the level of the trace of the equations of motion and its comparison with the f(R) case is discussed.