Some old and new results relating accuracy, stability and optimal bases are revisited. We focus on the relationship of these fields in the framework of totally positive bases and matrices. In fact, for some subclasses of totally positive matrices, which are often collocation, wronskian or gramian matrices of totally positive bases, high relative accurate algebraic algorithms have been found. Moreover, for spaces with a totally positive basis, the concept of B-bases corresponds to the optimally stable bases, and these bases also satisfy many other optimality properties, which play an important role in Approximation Theory and Computer Aided Geometric Design.