Quantum phase transitions describe the behaviour of quantum systems as a function of one or several control parameter(s), related to the interaction between the constituent particles. Of primary interest are the critical points where the system evolves from an 'ordered' into a 'disordered' phase with lower symmetry, reflected (in the infinite-size limit) by a non-analytic change in an order parameter. In nuclei, quantum phase transitions have been mostly studied in the context of algebraic models such as the interacting boson model. Irrespective of the successes or failures of this model to describe actual data, its Hamiltonian has been shown to display a rich variety of phase-transitional behaviour where the connections with phenomena or concepts such as coexistence, regular and chaotic motion, dynamical symmetries (exact or partial) and critical-point symmetries can be explored. Some recent advances in this field will be reviewed in this talk.