One possible explanation for the present observed acceleration of the Universe is the breakdown of homogeneity and isotropy due to the formation of non-linear structures. How the formation of non-linear structures and subsequent inhomogeneities affect the averaged cosmological expansion rate and may eventually lead to late-time acceleration is generally considered to be due to some backreaction mechanism. General Relativity together with dust matter scenarios have until recently been considered as the sole ingredients for averaged calculations. We shall present the backreaction formalism in more general scenarios, including imperfect fluids as well as alternative theories of gravity, and apply an averaging procedure to them in order to determine possible backreaction effects. The role of the frame choice and some paradigmatic classes of theories shall also be discussed.