Transit covers both human transportation (commuting and travel) and the transportation of goods around the world. It represents one of the largest sources of carbon in human society, from cars and trucks, to boats, to planes, to trains - it all costs energy, and the bulk of that energy, currently, comes from fossil fuels. This is an area where a lot of innovation is already taking place, but there's a lot more to be done.
Solar roadways could power the nation:
Solar Roadways is a company that is using solar power, engineering, and programming to create a new kind of road that could work for transportation, power generation, power transmission, internet, and emergency lighting all rolled into one!
Prototype solar-assisted bus:
California company is working on busses that, while not wholly solar, have their milage improved by a photovoltaic "boost".
Redesigning cities for bikes:
Lessons from a "brilliant" bike plan, showing how innovations in city planning, layout, and use can result in more efficient transit.