We discuss regularity for the crack set of a minimizer for the Griffith fracture energy, arising in the variational modeling of brittle materials. In the planar setting, we prove an epsilon-regularity result showing that the crack is locally a C^{1,1/2} curve outside of a singular set of zero Hausdorff measure. The main novelty is that, in contrast to previous results, no topological constraints on the crack are required. Joint work with Camille Labourie and Kerrek Stinson. This seminar is part of the activities of the Dipartimento di Eccellenza CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.