In recent years, the combinatorial systematic treatment of degenerations of classical linear series within the theory of tropical linear series has seen spectacular developments and has led to many important results on algebraic curves. On the other hand, the introduction and study of a number of tropical moduli spaces of curves along with its realization as skeletons of their classical (compactified) counterparts allows for a deeper understanding of combinatorial aspects of moduli spaces and in particular of their compactifications. In this talk, which is based on joint work with Lucia Caporaso and Marco Pacini, I will explore this principle for Cornalba's moduli space of spin spin curves. In particular, I will describe a stratification of this moduli space and introduce a tropical interpretation for the skeleton of its analytification. Time permitting, I will mention a number of interesting connections and applications of our work.