Scissors congruence is an equivalence relation on polytopes that we get by declaring two polytopes to be equivalent when we can cut one up and reassemble to get the other. The question of when two polytopes are equivalent under this relation is the subject of Hilbert's third problem, first addressed by Dehn in 1901. Later in the 20th century, Dupont and Sah approached the question of scissors congruence by building "scissors congruence groups" that encode this relation. Approaches to algebraic K-theory by Zakharevich allow us to define "higher scissors congruence groups" that encode not just whether polytopes are equivalent, but whether they are equivalent in different ways. I will discuss a new definition of higher scissors congruence groups that gives a natural map to group homology with which we can probe these groups. This work is joint with Gerhardt, Malkiewich, Merling and Zakharevich.