  We study ordered configuration spaces of compact manifolds with boundary. We
show that for a large class of such manifolds, the real homotopy type of the
configuration spaces only depends on the real homotopy type of the pair
consisting of the manifold and its boundary. We moreover describe explicit real
models of these configuration spaces using three different approaches. We do
this by adapting previous constructions for configuration spaces of closed
manifolds which relied on Kontsevich's proof of the formality of the little
disks operads. We also prove that our models are compatible with the richer
structure of configuration spaces, respectively a module over the Swiss-Cheese
operad, a module over the associative algebra of configurations in a collar
around the boundary of the manifold, and a module over the little disks operad.
