An overview of recent advances in the application of non-carbonaceous nanostructured and composite materials in hydrogen storage is presented in this review. The main focus is on complex hydrides, non-graphitic nanotubes, and other porous composite and framework materials since carbon nanotubes have been the subject of numerous other reviews. Recent advances in the area of alanates show a promising reversible absorption capability of up to 5%, closing in on the projected Department of Energy (DOE) target of 6%. Non-carbon nanotubes mainly showed a sorption capacity of 1-3 wt.-%, although a promising level of 4.2 wt.-% is shown by boron nitride nanotubes after collapse of their walls. Other interesting materials included here are lithium nitride and porous metallo-organic frameworks.