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Typical experiments on quantum systems rely on open-loop dynamics that is probed with projective measurements. We explore the use of the broader class of POVM measurements allowed within quantum theory both for real-time monitoring of quantum states and quantum control. In particular, we discuss unsharp measurements as a tool to probe dynamic correlation functions during quantum quench dynamics in many particle spin systems. We derive an unsharp measurement protocol applicable to arbitrary spin, and find the surprising result that projective measurements allow exact extraction of correlation functions in the case of spin 1/2. Secondly, I present a protocol for quantum state monitoring using sequential unsharp measurement that allows real-time state estimation with high fidelity. By combining measurement with feedback based on an a priori (potentially incorrect) assumption regarding the pre-measurement state, we show that one can drive the quantum state into the assumed state. We call this control by a self-fulfilling prophecy.