In solar cell research, the biggest recent breakthrough was probably the creation of efficient perovskite solar cells [1]. They're cheap, easy to make, and their efficiency in the lab is rising more rapidly than that of just about any other research cell since NREL began tracking (up from 3.5% in 2009 to 20.1% today) [2,3]. If their chemical stability problems can be resolved, they'll have big commercial applications.

[1] http://www.sciencemag.org/content/342/6165/1438.2

[2] http://www.nrel.gov/ncpv/images/efficiency_chart.jpg

[3] http://www.technologyreview.com/news/517811/a-material-that-...