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This paper develops the manifold T-splines, which naturally extend the concept and the currently available algorithms/techniques of the popular planar tensor-product NURBS and T-splines to arbitrary manifold domain of any topological type. The key idea is the global conformal parameterization that intuitively induces a tensor-product structure with a finite number of zero points, and hence offering a natural mechanism for generalizing the tensor-product splines throughout the entire manifold. In our shape modeling framework, the manifold T-splines are globally well-defined except at a finite number of extraordinary points, without the need of any tedious trimming and patching work. We present an efficient algorithm to convert triangular meshes to manifold T-splines. Because of the natural, built-in hierarchy of T-splines, we can easily reconstruct a manifold T-spline surface of high-quality with LOD control and hierarchical structure. [ABSTRACT FROM AUTHOR]