Synthetic (or biofuel) for aviation is of interest because, very simply, existing commercial aviation cannot exist without cheap and abundant liquid hydrocarbon fuels.
Already rising fuel costs have vastly affected the industry. US "peak aviation fuel" occurred in 1999. Peak departures was in 2005. 2012 consumption is _half_ of what was forecast in 2000, and departures 30% of the trend as of 2005 (even allowing for recession).
I first ran into this fact in January while looking into a biofuel "breakthrough" touted by Boeing (breakthrough or not it's wholly inadequate for needs): http://redd.it/1wo2hl
The departures data comes from a presentation by Steven Kopits made in February which I didn't come across until April: http://energypolicy.columbia.edu/events-calendar/global-oil-...
While passenger miles are still up, net, from 2000 levels, that's only on account of more efficient aircraft and higher load factors (that reduced legroom isn't just in your head).
So that's the problem scope.
Electricity is largely a solved problem: we can generate it with solar, wind, geothermal, hydro. Even nuclear for some bridging potential (though fuel availability even for thorium is decidedly limited as I calculate it http://redd.it/23nvqs).
Other than air travel, most transport needs are also tractable. Personal transport can be addressed via denser development, bicycles, electrified mass transit, personal electric vehicles, and other means. Rail can be electrified. Drayage (non-rail overland transport) is trickier, but might be addressed through EVs, biofuels, and even animal locomotion in a pinch.
Ocean shipping might return to use of sail or solid biofuel in the form of pelletized fuels.
But you cannot fly planes which carry appreciable cargos of people or freight useful distances reliably at speed without liquid fuels. So addressing that is of interest (an alternative would be to forgo flight or switch to lighter-than-air craft).
Personally I find the prospect of seawater-based fuel synthesis far more likely than air-based technologies: much richer carbon source, and likely far higher efficiencies.