  We study the cohomology of spaces of string links and braids in
$\mathbb{R}^n$ for $n\geq 3$ using configuration space integrals. For $n>3$,
these integrals give a chain map from certain diagram complexes to the deRham
algebra of differential forms on these spaces. For $n=3$, they produce all
finite type invariants of string links and braids.
