A novel aspect of recent experiments with quantum devices is that measurements can play an active role in preparing the state of the system, not just in diagnosing it. Unlike unitary evolution, the quantum collapse induced by local measurements can have a highly non-local impact on entangled quantum states, instantaneously destroying or creating new long distance correlations. This can lead to surprising collective effects such as measurement induced criticality and new kinds of universal structures in the post-measurement wave-function. I will first review recent progress in understanding these phenomena using mappings to effective statistical mechanical models. Next I will talk about the challenge of diagnosing the post measurement correlations experimentally. These correlations are so difficult to observe because they are conditioned on the outcome of many-measurements with exponentially small Born probability. I will preview a novel approach to resolve this post-selection problem by cross-correlating experimental data with results of classical computations.
