“…the approximants here considered are piecewise polynomials [18,19,21,76,77,82]. In particular, the aim of this paper is to collect the main results obtained by the authors, also in collaboration with other researchers, in such a topic, highlighting the approximation properties and the reconstruction of functions and data [3, 5, 6, 8-10, 26, 32-34, 36, 43, 45, 47, 57, 58, 67, 69-71], the applications in numerical integration and differentiation [22, 25, 27-31, 35, 37, 39-42, 44, 56, 68] and the numerical solution of integral and differential problems [2,13,24,38,46]. The above results can also be considered through spline dimension: 1D [2, 13, 25, 28, 29, 35-37, 39-42, 46, 57, 68], 2D [6, 8, 9, 22, 24, 26, 27, 30-34, 38, 43, 45, 56-58, 67, 70] and 3D [3,5,10,44,47,69,71].…”