I will discuss measurement-induced entanglement phase transitions in two classes of systems: (i) translation-invariant systems under post-selection and (ii) systems that are invariant under a global U(1) symmetry. In the former case, the transition can be understood as a form of many-body PT symmetry breaking. In the latter case, I will present evidence that a “charge-sharpening” phase transition occurs within the highly entangled phase, and summarize the critical properties of this transition.