Shape phase transitions in even and odd systems are reviewed within the frameworks of the Interacting Boson Model(IBM) and the Interacting Boson Fermion Model(IBFM), respectively and compared with geometric models when available. We discuss, in particular, the case of an odd j = 3/2 particle coupled to an even-even boson core that undergoes a transition from the spherical limit U(5) to the gamma-unstable limit O(6). Energy spectrum and electromagnetic transitions, in correspondence of the critical point, display behaviors qualitatively similar to those of the even core and they agree qualitatively with the model based on the E(5/4) boson-fermion symmetry. We describe then the U-BF(5) to SUBF(3) transition when a fermion is allowed to occupy the orbits j = 1/2, 3/2,5/2. The additional particle characterizes the properties at the critical points in finite quantum systems.