  A hypergraph $H$ is called universal for a family $\mathcal{F}$ of
hypergraphs, if it contains every hypergraph $F \in \mathcal{F}$ as a copy. For
the family of $r$-uniform hypergraphs with maximum vertex degree bounded by
$\Delta$ and at most $n$ vertices any universal hypergraph has to contain
$\Omega(n^{r-r/\Delta})$ many edges. We exploit constructions of Alon and
Capalbo to obtain universal $r$-uniform hypergraphs with the optimal number of
edges $O(n^{r-r/\Delta})$ when $r$ is even, $r \mid \Delta$ or $\Delta=2$.
Further we generalize the result of Alon and Asodi about optimal universal
graphs for the family of graphs with at most $m$ edges and no isolated vertices
to hypergraphs.
