Dehn answered Hilbert's third problem around 1900 by showing that certain tetrahedra are not scissors-congruent to a cube. I will explain progress towards the problem of parametrizing all tetrahedra that are scissors-congruent to a cube. This is based on joint work with Kiran Kedlaya, Alexander Kolpakov, and Michael Rubinstein, and further work of two former MIT undergraduates, A. Anas Chentouf and Yihang Sun.