The inherent probabilistic nature of quantum mechanics places particular importance on the concept of quantum measurements. My interests lie in the interplay of the effect of measurements on a quantum state and unitary quantum dynamics. Measuring a quantum degree of freedom generally collapses its state to one of the eigenstates of the observable being measured with the Born rule probability. This disetangles the measured degree of freedom from the rest of the system and leads to a loss of coherence in the dynamics. The competition between entangling unitary dynamics and dientangling measurements is an interesting problem in statistical mechanics as well as in quantum information theory. Another setting is to consider a measurement apparatus weakly coupled to the system, and measuring the apparatus after decoupling it from the system. However, since the quantum dynamics prior to the measurement entangles the apparatus with the system, measuring the former non-trivially affects the state of the latter. This seemingly undesirable affect can be turned to an advantage by designing appropriate protocols that allow us to steer quantum systems towards correlated states or realise novel phases via measurements. In the time-continuum limit, systems undergoing continuous measurements can be described using a Lindblad equation which arises also in the context of open quantum systems in contact with Markovian environments.