International audienceWe explore T-splines, a generalization of NURBS enabling local refinement, as a basis for isogeometric analysis. We review T-splines as a surface design methodology and then develop it for engineering analysis applications. We test T-splines on some elementary two-dimensional and three-dimensional fluid and structural analysis problems and attain good results in all cases. We summarize the current status of T-splines, their limitations, and future possibilities