We present a brief review of research topics of current interest that depend on an algebraic approach to molecular bending dynamics. This approach is based on a u(3) spectrum generating algebra. In particular, we briefly present results on three topics: the calculation of finite-size analytical corrections to mean field results, the application of the model to the large-amplitude vibrational bending mode of the NCNCS molecule, and the analysis of the influence of quadratic Casimir operators on excited state quantum phase transitions. © Published under licence by IOP Publishing Ltd.