It is widely believed that quantum physics is a fundamental theory describing the Universe. As such, one would expect to be able to see how classical physics that is observed in the macroscopic world emerges from quantum theory. This has so far largely eluded physicists, due to the inherent linear nature of quantum physics and the non-linear behaviour of classical physics. One of the principle differences between classical and quantum physics is the statistical, probabilistic nature of quantum theory. It is from this property that non-classical states can arise, such as entangled states. These states possess maximal correlations. However, they are not the only way in which correlations are created in quantum systems. This thesis aims to show how open quantum systems naturally contain correlations from their quantum nature. Moreover, even seemingly simple open quantum systems can behave far more complexly than expected upon the introduction of quantum feedback. Using this effect, the dynamics may become non-linear and as such behave non-trivially. Furthermore, it is shown how these effects may be exploited for a variety of tasks, including a computational application in hidden quantum Markov models and a quantum metrology scheme that does not require the use of exotic quantum states. This results in the design of systems that benefit from the use of quantum mechanics, but are not constrained by the use of experimentally difficulties such as entanglement.