The departure tax for leaving Bangladesh by air is included in the price of air tickets.
It's easiest to fly to Australia on board carriers such as Thai, Tiger Airways or Air Asia, which go via Bangkok, Singapore and Kuala Lumpur respectively.
There are plenty of flights linking Dhaka with European countries such as Germany, Italy and the Netherlands, which go via Dubai, Istanbul or Kolkata.
There are basically two ways to get to Bangladesh from the USA. From the west coast, virtually everyone flies to Dhaka via Bangkok or Singapore. You can also fly direct to India and connect from there, but it may cost more. From the east coast, most people fly via Europe.
You should get some well-priced fares to and from London, mostly via the Middle East. Biman Bangladesh, the country's national carrier, incidentally has direct flights to London from Dhaka, and can sometimes give you the best deal despite not guaranteeing you the most luxurious flying experience.
There are three international airports in Bangladesh:
Dhaka Hazrat Shahjalal International Airport (DAC; www.shahjalalairport.com)
Chittagong Shah Amanat International Airport (CGP)
Sylhet Osmani International Airport (ZYL)
In practice, the vast majority of foreign visitors arrive at Dhaka’s Hazrat Shahjalal International Airport. It’s pretty basic for a capital-city airport but it has money-changing facilities, including ATMs that accept foreign cards, some duty-free shops and a couple of restaurants.
There’s an official taxi rank, although it’s cheaper to try your luck with taxis and CNGs (auto-rickshaws) outside. The 30-minute haul to Banani, the first prominent residential neighbourhood on your way into the city, will cost you Tk 750 by taxi or Tk 300 by CNG. If you ask your hotel for an airport pick-up, expect to pay around Tk 1000.
The unofficial airport website has a useful flight-status feed.
Biman (www.bimanairlines.com) is the national carrier of Bangladesh. It's a scruffy and curiously disorganised operation, but the fleet is fairly well maintained and the airline has a good safety record.
There are direct flights to/from all nearby Asian countries. Most connections are through Dhaka, from where you can get particularly cheap flights to Thailand, Malaysia, India, China and the Middle East. It is also possible to use Chittagong airport for India and Thailand. Sylhet’s airport has occasional international flights such as those to Mecca during the Hajj pilgrimage.