Given an $r$-uniform hypergraph $\mathcal{A} \subset X^{(r)}$, the (lower) shadow of $\mathcal{A}$, denoted $\delta(\mathcal{A})$ is defined as $\delta(\mathcal{A}):= \{ B \in X^{(r-1)} : B \subset A \text{ for some } A \in \mathcal{A} \}$. In this talk, we will explore the classical Kruskal-Katona theorem which gives a lower bound on $|\delta(\mathcal{A})|$ and describe related notions of colex order and compression operators on set families.