  Nowhere dense graph classes provide one of the least restrictive notions of
sparsity for graphs. Several equivalent characterizations of nowhere dense
classes have been obtained over the years, using a wide range of combinatorial
objects. In this paper we establish a new characterization of nowhere dense
classes, in terms of poset dimension: A monotone graph class is nowhere dense
if and only if for every $h \geq 1$ and every $\epsilon > 0$, posets of height
at most $h$ with $n$ elements and whose cover graphs are in the class have
dimension $\mathcal{O}(n^{\epsilon})$.
