Continuously monitored quantum systems can undergo "entanglement transitions" in their steady states (conditioned on the measurement outcomes). I will briefly review our understanding of entanglement transitions and why it is challenging to observe them in realistic experiments. I will introduce a variant on the entanglement transition, called the "charge sharpening" transition, and explain how it can be related to a transition in the ability of an eavesdropper to "learn" the state of a system using local measurements.