I will give an overview of the timescape cosmology. It is assumed that inhomogeneities - voids, walls and filaments - modify the average background geometry of the universe, which is no longer a simple solution of Einstein's equations with homogeneous dust. The Buchert statistical formalism with backreaction in general relativity is reinterpreted by revisiting fundamental principles relating to the definition of gravitational
energy in a complex geometry. Cosmic acceleration is realized as an apparent effect due to the the relative calibration of the asymptotic clocks of observers in gravitationally bound structures relative to the time parameter that best describes average statistical evolution. The cosmic coincidence problem is solved directly in relation to the growth of the void fraction. An observationally viable cosmology without dark energy has been developed, with many predictions that are very close to the standard cosmology, but with differences which can be tested. I will outline current observational constraints, future tests (e.g., with the Euclid satellite), and also the current theoretical challenges that need to be overcome for the timescape model to fully compete with the Lambda Cold Dark Matter cosmology at every level.