I will discuss a theory of connections for bundle of ideals in a Lie groupoid. This theory generalizes the usual theory of principal bundle connections and has an infinitesimal counterpart at the Lie algebroid level. Applications of this theory range from (i) obtaining representatives in rational cohomology for the Dixmier-Douady class of a gerbe to (ii) constructing linear models for Poisson structures around Poisson submanifolds. This talk is based on the preprint arXiv:2204.08507, joint with Ioan Marcut (Radboud Universiteit Nijmegen).