The cytoskeleton is an inhomogeneous network of semi-flexible filaments involved in a variety of active biological processes. Although cytoskeletal filaments, particularly microtubules, are very stiff and can be embedded in a dense and cross-linked network, they have been shown to typically exhibit significant bending at all length scales in cells. In my talk, I will introduce a model of a semi-flexible filament which is deformed and twisted by different types of active cross-linkers, and subjected to thermal fluctuations. Using this approach, we determine the bending spectrum for different realizations of the external forces. We show that active fluctuations generically lead to a q^-4 dependence of the bending spectrum. Furthermore, we discuss an approach to estimate the torsional rigidity of microtubules.