**Abstract:** For a graph $F$, we say a hypergraph $H$ is Berge-$F$ if it can be obtained from $F$ be replacing each edge of $F$ with a hyperedge containing it. We say a hypergraph is Berge-$F$-saturated if it does not contain a Berge-$F$, but adding any hyperedge creates a copy of Berge-$F$. The $k$-uniform saturation number of Berge-$F$, $\mathrm{sat}_k(n,\text{Berge-}F)$ is the fewest number of edges possible over all Berge-$F$-saturated $k$-uniform hypergraphs on $n$ vertices.

In this talk we will explore some specific saturation numbers for Berge hypergraphs. We will also see that at least for small uniformities, these numbers grow linearly with $n$, extending a classical result of Kászonyi and Tuza. Finally, we will mention many interesting open problems in this area of research.