The ability to control and measure properties of quantum many-body systems has reached a new level of experimental accuracy. Generically, the unitary time evolution of a quantum many-body system couples its microscopic constituents leading to a highly entangled quantum state. On the other hand, performing a global measurement to learn something about the physical content of the system will collapse the wavefunction, destroying any entanglement. However, if a quantum system undergoing unitary time evolution is measured locally at a small but non-zero rate, it was recently discovered that the highly entangled state survives. Only after a critical measurement rate will the wavefunction essentially collapse leading to a measurement induced phase transition in the structure of the entanglement. In this talk, we will discuss our work to understand the universal nature of measurement and control induced phase transitions in random quantum circuits. First, the properties of the underlying conformal field theory at the measurement induced transition are studied allowing us to identify 3 distinct universality classes, depending on the quantum nature of the gates. Second, we show how this transition is unstable to static disorder, which flows to an infinite randomness fixed point. Last, using post selection and feedback we identify a control induced phase transition that is concomitant with an entanglement transition but lies in a diffusive, and hence distinct, universality class.