Many of the most relevant observables of matter depend explicitly on atomistic and electronic details, rendering a first principles approach to computational materials design mandatory. Alas, even when using high-performance computers, brute force high-throughput screening of material candidates is beyond any capacity for all but the simplest systems and properties due to the combinatorial nature of compound space, i.e. all the possible combinations of compositional and structural degrees of freedom. Consequently, efficient exploration algorithms exploit implicit redundancies and correlations. I will discuss recently developed statistical learning based approaches for interpolating quantum mechanical observables throughout compound space. Numerical results indicate promising performance in terms of efficiency, accuracy, scalability and transferability.