Links between blossoms and optimal bases are studied, in a general context [cf. M.-L. Mazure, Comput. Aided Geom. Design 16, 649–669 (1999; Zbl 0997.65022)]. The total positivity of the Bernstein basis follows from the properties of the polynomial blossoms, and its optimality from their geometrical meaning is shown. An extension to the Chebyshev and quasi-Chebyshev framework is given with examples of optimal normalized totally positive bases in this context. In the framework of Chebyshev or quasi-Chebyshev splines with connection matrices, it is shown that the existence of blossoms automatically leads to B-spline bases, which are the corresponding optimal normalized totally positive bases.