In this thesis, I present methods and techniques for the study and use of non- stationary quantum phenomena in cavity quantum electrodynamics and optomechanics. Thus, I introduce a multiple-scale perturbation technique that allows us to find excellent approximate solutions to time-local master equations describing open quantum systems, both in the stationary and nonstationary regimes. The technique provides the time-evolution of the corresponding dynamical map and, consequently, the time-evolution of the system density matrix for arbitrary initial conditions, allowing us to identify in each order the characteristic time scales involved in the problem. Furthermore, I present a nonstationary protocol for the sensing of a classical force driving a mechanical oscillator coupled to an electromagnetic cavity under two-tone driving. The applied force shifts the position of the mechanical oscillator, whose change can be monitored through the output electromagnetic field. For the purpose of analysing the force sensitivity quantitatively, I develop a theoretical framework based on the signal-to-noise ratio of linear spectral measurements, stationary or nonstationary, and I determine the conditions for optimal sensitivity. The results presented here open the door to the exploration of new forms to enhance quantum effects far from the traditional stationary regime.