given an $r$-uniform hypergraph $h$ and an $r$-uniform hypergraph $f$, define the relative tur\'an number $ex(h,f)$ to be the maximum number of edges in an $f$-free subgraph of $h$. in this talk we discuss bounds for $ex(h,f)$ when $f$ is a loose cycle, berge cycle, and a complete $r$-partite $r$-graph when the host $h$ is either arbitrary or when it is the random hypergraph $h_{n,p}^r$. \\ \\ this is joint work with jiaxi nie and jacques verstraete.