Explaining supernova distances without Dark Energy: voids and Swiss Cheese

The most widely applied cosmological model needs to invoke Dark Energy or a Cosmological Constant to be able to explain the observed distances to supernovae at high redshifts. However, as Dark Energy has some flaws from a theoretical point of view, many attempts are made to explain the distance-redshift relation in a universe containing only baryonic and dark matter. I overview some models in which the distribution of matter is so far from perturbative, that it can potentially explain the observed distance-redshift relation. When we are living in a large local void, or in the limit where the universe is saturated with voids and structures (Swiss Cheese), we can observe the distance-redshift relation as we see it today, even without an accelerated expansion of the whole universe. Then I point out difficulties and weaknesses for these models, and show why they may or may not be a viable alternative to Dark Energy.