This thesis comprises of investigations relating to the creation, manipulation, and detection of quantum states in specific configurations of optomechanical and circuit QED systems. Both the unconditional and conditional master equation formalisms are employed toward this end. In the optomechanical context, the “membrane-in-the-middle” system is investigated with regard to its various experimentally demonstrated parametric couplings between optical fields and membrane displacement. Via these couplings, the optical fields are functionalized as probes and controls of the quantum state of a mechanical membrane vibrational mode. In one case, continuous measurement of the optical field is shown to both induce and detect quantum jumps of mechanical energy; the conditions under which this occurs are established and verified in numerical simulations. In a separate case, a scheme is developed that employs simultaneous continuous measurement of two optical fields with distinct parametric couplings to the mem- brane. In this case, it is shown that in situ monitoring and control of the quantum noise profile of a mechanical mode becomes possible. Specifically, the variance of the mechanical energy dis- tribution is numerically shown to monotonically decay with increasing measurement strength of one of the optical fields. In the circuit QED setting, a many-body system is proposed compris- ing of microwave coplanar waveguide resonators arranged in a one-dimensional lattice. Each of the resonators contains a tuneable Kerr nonlinearity that provides an attractive interaction energy for the microwave quanta in the lattice, and each of the resonators is tuneably coupled to its nearest neighbours in the lattice. A scheme is developed under which the tuneability of the parameters is used to effect quantum phase transitions such that initially local microwave resonator quantum states become non-locally superposed across the whole system, thereby providing a feasible route toward deterministically entangling complex microwave resonator states across forty or more resonators. Numerical simulations of the scheme are performed to demonstrate its effectiveness under experimentally accessible parameters.