Quantum correlations and quantum coherence are not only recognised as fundamental features in the quantum regime that depart from the classical world, but also regarded as useful resources in numerous quantum information processing tasks. Thus, characterising and quantifying these quantum properties is a prime task in quantum information theory. In this thesis, I study the following problems: How could quantum coherence be extracted from a set of measurements? How are quantum correlations distributed among multi-party quantum systems? Are there tradeo relations such that these quantum features cannot be freely extracted or shared? Part I is devoted to investigating the quanti cation of quantum coherence with respect to a set of measurements. I rst use two valid coherence measures, the l1-norm and relative entropy of coherence, to study the tradeo s between the coherences of mutually unbiased bases, and derive a complementarity relation for qubit coherences. Then, I propose using the average coherence to measure the intrinsic coherence of a quantum state, and obtain useful bounds for average coherence measures. In Part II, I nd two new invariance properties, isotropic and anisotropic invariance quantities, for pure three-qubit states. These properties are proven useful in studying distributed quantum correlations, and results include a strong monogamy relation for Bell nonlocality, Einstein-Podolsky- Rosen inequalities, geometric discord, and delity of remote state preparation (some are generalised for arbitrary three-party states), tradeo relations for anisotropic invariants, 3-tangle, and Bell nonlocality for three-qubit states, and a universal ordering of pairwise quantum correlation measures for pure three-qubit states. In Part III, I investigate the quantum monogamy phenomenon in terms of volumes of quantum steering ellipsoids. I derive a volume monogamy relation for all three-qubit states, and then generalise it for multi-qubit states. Then, the incomplete steering phenomenon is examined and a method to characterise and quantify it for two-qubit states is proposed. Finally, I generalise this to investigate whether there is a monogamy relation for the incomplete steering of the inner party for pure qubit-qubit-qudit states.