Accelerating the discovery of new materials with tailored properties is essential to address societal challenges in green energy transformation and sustainability. Modern chemically and structurally complex alloys hugely expand chemical composition space, promising materials designers an unprecedentedly-large parameter space for materials discovery. A challenge in navigating and exploiting such high-dimensional configuration spaces is that conventional approaches that require sampling huge numbers of example configurations become unfeasible for both experiment and available computational approaches. We have therefore developed data-driven and descriptor-based approaches, which combine ab initio methodology with machine learning approaches. These combined approaches provide powerful frameworks to overcome these issues enabling new design strategies in handling chemical and structural complexity. Applications of such approaches to the discovery of mechanically superior alloys, hard magnets, and materials related to electrocatalysis and corrosion science will be discussed.