In a closed system, thermalization occurs through unitary evolution, which transfers information encoded in the initial state into increasingly nonlocal degrees of freedom. Recent work on random quantum circuits has clarified how this non-local encoding is affected by an external observer: at a critical measurement rate the system undergoes a phase transition from an encoding state with volume law entanglement to an area law state. I will review the current understanding of the transition using a mapping to statistical mechanics models and use this description to predict new phenomena. First, I will argue that large scale entanglement, with sub-volume critical power law scaling, remains in the monitored system when it is coupled to a decoherence channel at its edge. Second, I will show that the capacity of certain quantum circuits to facilitate quantum teleportation over infinite distances has a critical onset at a finite time.