Inhomogeneous, relativistic cosmology has recently observed a rise in popularity among the cosmologists. In particular, the scalar averaging approach (Buchert formalism) has been intensively examined
both analytically and numerically, giving some new insights
into the problem of cosmological backreaction i.e. the conjectured influence of small scale density inhomogeneities on the large scale evolution of the Universe. In my talk, I will summarise these recent efforts, including multi-scale partitioning approach and some results from N-body simulations. I will also put into perspective future prospects of cosmological backreaction investigations.