NURBS surface modeling stands as the international standard in conventional industrial product design. However, its local subdivision capability often incurs redundant computations owing to its tensor product structure, leading to limitations in achieving satisfactory local subdivision during NURBS surface modeling. In contrast, splines on T-mesh represent a distinct class of splines characterized by their local subdivision properties. Notably, the bicubic first-order smooth splines defined on the hierarchical T-mesh by our research group, referred to as "Chinese splines" by the international community, exhibit favorable attributes for adaptively addressing geometric modeling challenges. Our research group is particularly focused on exploring spline functions on T-mesh, with emphasis on several key aspects: determining the dimension and stability of spline spaces on T-mesh, constructing base functions, applying geometric analysis techniques such as curve and surface fitting, quasi-interpolation, and addressing associated challenges such as various matrix assembly problems.