Crystal skeletons were introduced by Maas-Gariépy in 2023 by contracting quasi-crystal components in a crystal graph. On the representation theoretic level, crystal skeletons model the expansion of Schur functions into Gessel's quasisymmetric functions. Motivated by questions of Schur positivity, we provide a combinatorial description of crystal skeletons, and prove many new properties, including a conjecture by Maas-Gariépy that crystal skeletons generalize dual equivalence graphs. We then present a new axiomatic approach to crystal skeletons. We give three versions of the axioms based on GL_n-branching, S_n-branching, and local axioms in analogy to the local Stembridge axioms for crystals based on novel commutation relations. This is based on joint work with Sarah Brauner, Sylvie Corteel and Zajj Daugherty (arXiv:2503.14782).