  Degeneracy plays an important role in understanding Tur\'an- and Ramsey-type
properties of graphs. Unfortunately, the usual hypergraphical generalization of
degeneracy fails to capture these properties. We define the skeletal degeneracy
of a $k$-uniform hypergraph as the degeneracy of its $1$-skeleton (i.e., the
graph formed by replacing every $k$-edge by a $k$-clique). We prove that
skeletal degeneracy controls hypergraph Tur\'an and Ramsey numbers in a similar
manner to (graphical) degeneracy.
  Specifically, we show that $k$-uniform hypergraphs with bounded skeletal
degeneracy have linear Ramsey number. This is the hypergraph analogue of the
Burr-Erd\H{o}s conjecture (proved by Lee). In addition, we give upper and lower
bounds of the same shape for the Tur\'an number of a $k$-uniform $k$-partite
hypergraph in terms of its skeletal degeneracy. The proofs of both results use
the technique of dependent random choice. In addition, the proof of our Ramsey
result uses the `random greedy process' introduced by Lee in his resolution of
the Burr-Erd\H{o}s conjecture.
