The principle of superposition is one of the main building blocks of quantum physics and has tremendous consequences both for our fundamental understanding of nature and for technological applications. In particular, the existence of coherent superposition leads to the concept of unavoidable quantum uncertainty. The role played by this "coherent" uncertainty within thermodynamics, as well as its relationship to classical lack of knowledge, is the main subject of this thesis. In Part I we study thermodynamic limitations of processing quantum coherence within a resource-theoretic framework. Using the time-translation symmetry that arises from the first law of thermodynamics, we find constraints on possible manipulations of coherence and prove their irreversibility due to the second law. We also generalise to the quantum domain Szilard's concept of converting information into work. Namely, we show how, in the presence of a heat bath, coherence of a system can be exploited to perform mechanical work. Finally, we analyse the effect that coherence has on the structure of the thermodynamic arrow of time, i.e., on the set of states into which a given state can freely evolve under thermodynamic constraints. In Part II we focus on the interplay between quantum and classical uncertainty manifested in uncertainty relations. We show that separating the total uncertainty into these two distinct components leads to a new type of "fixed-entropy" uncertainty relation. We also analyse how classical ignorance affects the structure of states that minimise the unavoidable uncertainty arising from the noncommutativity of two observables. Finally, we study error-disturbance trade-off relations and, by proving that quantum uncertainty can be simultaneously maximised for any two observables, we clarify the unphysical nature of state-dependent relations.