Holography has taught us that spacetime is emergent and its properties depend on the entanglement structure of the dual boundary theory. At the same time, we know that local projective measurements tend to destroy entanglement. This leads to a natural question: what happens to the holographic bulk spacetime if we perform strong local projective measurements on a subsystem $A$ of the boundary? In particular, I will explain the effect of measurements performed both on subsystems of a single CFT in its vacuum state, which is dual to pure AdS spacetime, and on various subsystems of two copies of a CFT in the thermofield double state, which is dual to a double-sided AdS black hole. The post-measurement bulk is cut off by end-of-the-world branes and is dual to the complementary unmeasured subsystem $A^c$. The measurement triggers an entangling/disentangling phase transition in the boundary theory, corresponding to a connected/disconnected phase transition in the bulk dual geometry. Interestingly, the post-measurement bulk includes regions that were part of the entanglement wedge of $A$ before the measurement, signaling a transfer of information from the measured to the unmeasured subsystem analogous to quantum teleportation. Finally, I will discuss open questions and future directions related to our work, with a particular focus on its consequences for the complexity of bulk reconstruction.