These lecture notes review the theoretical problems associated with coarse-graining the observed inhomogeneous structure of the universe at late epochs, of describing average cosmic evolution in the presence of growing inhomogeneity, and of relating average quantities to physical observables. In particular, a detailed discussion of the timescape scenario is presented. In this scenario, dark energy is realized as a misidentification of gravitational energy gradients which result from gradients in the kinetic energy of expansion of space, in the presence of density and spatial curvature gradients that grow large with the growth of structure. The phenomenology and observational tests of the timescape model are discussed in detail, with updated constraints from Planck satellite data. In addition, recent results on the variation of the Hubble expansion on <∼ 100h−1Mpc scales are discussed. The spherically averaged Hubble law is significantly more uniformin the rest frame of the Local Group of galaxies than in the conventional rest frame assumed for the Cosmic Microwave Background. This unexpected result supports a fundamental revision of the notion of the cosmic rest frame, consistent with the expectations of the timescape scenario.