Quadrature rules play a fundamental role in several numerical applications and, in particular, in finite element analysis and isogeometric analysis. Using classical quadrature rules designed for polynomials as element-wise quadrature rules for smooth splines is a feasible and common approach. However, this strategy might nullify, or at least significantly reduce, the advantage of smooth splines because the intrinsic smoothness of the spaces is ignored, resulting in a too high computational cost. In this talk we focus on triangular spline finite elements based on the well-known Clough–Tocher and Powell–Sabin splits. Besides presenting ad hoc (optimal) quadrature rules, we identify quadrature rules for polynomials on triangles that remain exact for sufficiently smooth spline spaces sharing the same degree defined on such splits. Our analysis is based on the representation of the considered macro-elements in terms of suitable simplex splines, and offers insights that can be further extended to the three-dimensional case. This talk is based on joint works with Salah Eddargani, Tom Lyche, and Carla Manni.