There are boat services to Batumi and Poti from Istanbul and Odessa. At the time of writing the Turkish Black Sea port of Trabzon was closed to passenger services. Be also aware that Georgian port of Sukhumi is closed for any cargo or passenger boats apart from those with humanitarian purposes. All vessels going to Sukhumi must undergo border check with Georgian coast guard in nearby port of Poti.
There are flights to Tbilisi from a number of European, North American and Asian cities, including London bmi (http://www.flybmi.com), Paris Georgian Airways (http://www.airzena.com/), Vienna Austrian Airlines, Warsaw LOT Airlines, Kiev Georgian Airways, Munich Lufthansa, Athens Georgian Airways, Riga airBaltic, (http://www.airbaltic.com), Istanbul Turkish Airlines, Prague Czech Airlines. Just recently, KLM cancelled their flights to Tbilisi but you can fly with Georgian Airways from/to Amsterdam. Belavia Belarusian National Airlines (http://www.belavia.by) is now offering daily direct flights from Minsk to Tbilisi at great rates, and there are plenty of connecting flights from European cities to Minsk, e.g. from Amsterdam transit visa is not required if you fly to Georgia. Please note that Georgian Airways AirZena (http://www.airzena.com/) has many flights from many different cities. See also airBaltic for cheap flights to many European destinations.
May 26, 2007 saw the reopening of the airport in Batumi. Turkish Airlines (http://www.thy.com) flights run every day between Batumi and Istanbul. Other destinations serviced by the Batumi airport include Kharkov, Kiev and from 15 September 2010 - Minsk twice per week with Belavia. The Batumi airport is located about 10km south of the city center and is accessible by minibus and taxi.
Flights to Moscow and other Russian cities are still irregular, given the current state of affairs between two countries.
Rapidly expanding touristic infrastructure Black sea resorts along Georgian coastline, ski resorts in the mountains of subtropical Ajara region and in Svaneti led to opening more international airports most recently in ski resort of Mestia, and along with recent ranking as one of the safest countries in Europe and rapidly improving infrastructure, the number of tourists is increasing exponentially.
There are many minibuses sing. samarshruto taxi; pl. samarshruto taxebi that operate international routes to and from cities and large towns in Georgia. Minibuses run between Georgia and Russia and despite the current state of affairs between two countries, are more reliable and more accessible than the often irregular flights to Russia, Azerbaijan, Armenia, Iran, and Iraq. In Tbilisi, these routes usually originate and terminate at bus stations and the Didube subway station. Outside Tbilisi, minibus routes may stop at either bus stations or central locations town squares.
There are train services from Baku, Azerbaijan which stop at various places on the route and terminate in Tbilisi. Note that the "BP train" has been canceled. Construction of railroad linking the Turkish town of Kars to Baku, Azerbaijan-including both a new line and modernization of existing lines-is underway and will be finished sometime between 2010-2012. This will establish a direct link from Tbilisi to Istanbul and farther to Europe as well as a faster, more comfortable ride into Azerbaijan.Also, there's service from Yerevan, Armenia.