Solving partial differential equations on domains with smooth boundaries with standard finite element methods will usually lead to discretization errors. Since the un- derlying domain is often the result of CAx-modelling via B-splines, the ansatz of using these functions as finite element functions was introduced, see e.g. [1]. Since then, various different techniques involving local refinement were developed, such as locally refined (LR) B-splines [2], hierarchical B-splines (HB-splines) [3], truncated HB-splines (THB-splines) [4], and T-splines [7]. Each solution to adpative refinement yield locally linear independent basis functions, given certain conditions. For LR B-splines and (T)HB-splines, this condition is given within the refinement process, i.e. during the refinement process the case of linear dependent splines has to be resolved, see e.g. [5, 6]. For T-splines, this is given by a geometric condition on the mesh, see e.g. [8]. Thus, a refinement technique for T-splines has been introduced that sustains locally linear independent basis functions. [...] In this talk, we present deal.t, an isogeometric framework to solve PDEs with no dis- cretization errors through T-splines. We will give a short introduction to the basics of T-splines, i.e. the definitions and the necessary geometric condition for linear indepen- dency. The process of Bezier extraction for T-splines will be addressed shortly, which is derived from standard Bezier extraction techniques for B-splines, see also [12]. Involved in the definitions regarding T-splines and an effective implementation without redundant data, are various different meshing classes. We will give a short overview of these meshes to explain our strategy for deal.t. The talk will finish in a few examples with code-snippets to demonstrate the usage of the new framework. These will also be compared tostandard FEM results.