It looks like Georgia has been making a big effort in marketing itself as a tourist-friendly country (for example no visas are required, most signs and indications are in English in addition to being in Georgian, there is free public wi-fi in the most central areas of the capital...) and the efforts are starting to pay-off. Foreign tourist arrivals are increasing in Georgia and so is the number of airlines that have started flying to the Caucasian country or are planning to do so, such as Aegean Airlines, Qatar Airways (via Baku), FlyDubai or Alitalia. In the meantime, Turkish Airlines seem to have the upper hand when it comes to connecting the country with the rest of the world (Tbilisi airport is also run by a Turkish company, TAV, that manages also Istanbul's impressive Ataturk airport).
One curious fact is that, contrarily to what happens at most European airports, it seems that most activity happens during the early hours of the morning, between midnight and 4am. This is the time when several scheduled flights arrive: Turkish Airlines from Istanbul, BMI (soon to be replaced by BA) from London (via Baku), Aerosvit from Kiev, Lufthansa, from Munich...
These schedules make sense when you take into account Tbilisi's geographical position, most of these airlines can extract an extra rotation from the aircraft by flying it to Tbilisi at night, gathering feeding passengers throughout the afternoon at their more westerly hubs and then feeding their westward-routes early in the morning with the return flight.
One of Airzena's Boeing 737s
When it comes to local airlines, Airzena is Georgia's national airline and, although its network and schedules are currently somewhat limited, the flag carrier currently has several Boeing 737-NGs and 787s on order. It looks like Airzena is betting on the steady growth of the Georgian tourism industry, the Dreamliners order might be an indication that it is also looking to start flying long-haul (possibly to the US?)
Another Georgia-based airline is Sky Georgia, although currently focused on cargo only and with no scheduled passenger flights, according to Wikipedia, you can still this dilapidated DC-9 next to Tbilisi airport's runway...
Two new airlines are starting soon FlyGeorgia and Air Caucasus, and low cost airline Wizz Air is also starting flights to second-largest city Kutaisi. In short, a market that is really taking-off!
And, once you are in Georgia, if you wish to visit the country from a privileged angle and have some spare cash, you can buy this Mil Mi-8 VIP helicopter, apparently on sale on Alibaba.com!