Computational electronic-structure calculations of nanoscale systems are powerful tools which provide fundamental insight, help interpret experiment results, and ultimately aid the development of new materials. Density functional theory (DFT) dominates this field, and has had an enormously beneficial impact on nanoscience. However, there are still many situations in which present DFT fails to provide accurate quantitative predictions. The development of methods which provide more reliable predictive power is a growing field, and these approaches are becoming practical alternatives to DFT for nanoscience applications. In this article, we review four promising alternatives: Diffusion Monte Carlo, domain-based local pair natural orbital coupled cluster, the time-dependent formulation of DFT, and the GW method. We provide descriptive overviews of each method, accompanied by examples of where they have been applied to problems relevant to nanoscience, and discuss the major challenges they currently face as well as the outlook for the future. Between them these methods comprise a flexible toolkit whose continued development will be a big step towards the reliable computational design of new materials.