  We define decorated $\alpha$-stable trees which are informally obtained from
an $\alpha$-stable tree by blowing up its branchpoints into random metric
spaces. This generalizes the $\alpha$-stable looptrees of Curien and
Kortchemski, where those metric spaces are just deterministic circles. We
provide different constructions for these objects, which allows us to
understand some of their geometric properties, including compactness, Hausdorff
dimension and self-similarity in distribution. We prove an invariance principle
which states that under some conditions, analogous discrete objects, random
decorated discrete trees, converge in the scaling limit to decorated
$\alpha$-stable trees. We mention a few examples where those objects appear in
the context of random trees and planar maps, and we expect them to naturally
arise in many more cases.
