Post-war up to the late 1970s this was a cosy situation with national carriers setting the prices, and travel was mostly by rich, famous, and business travelers.
In 1977 Laker Airways became the second long-haul, low-cost, "no frills" airline, operating low-fare scheduled services using McDonnell Douglas DC10s between London Gatwick Airport and New York's John F. Kennedy Airport (after pioneering Icelandic low-cost carrier Loftleiðir).
The company did not survive the recession of the early 1980s and operated its last flight on 5 February 1982, the day it went bankrupt.
Since then we have in UK & Europe had the rise of Easyjet, founded in 1995 by Stelios Haji-Ioannou and based initially out of London Luton airport.
In 2015 for the busy and lucrative route from Europe to Australia and New Zealand you have the option of multiple airlines/routes. From London Heathrow for example of Singapore Airlines via Singapore, Etihad Airways via Abu Dhabi, Emirates Airline via Dubai, Cathay Pacific via Hong Kong, Virgin Australia via Dubai, and Malaysia Airlines via Kuala Lumpar (though after two crashes in 2014 maybe not), and British Airways and Qantas (both either via Singapore or Dubai). There are many more to consider but if you are tall (1 am 6ft 4in) then be careful of your Chinese or Japanese airlines as the seats in economy can be based on smaller/shorter passengers.
Sometimes the cheapest option on long-haul flights is one having two stopovers with Royal Brunei Airways on the route between London Heathrow and Melbourne for example, stopping at both Dubai and Brunei (Bandar Seri Begawan). The benefit of this route is both flying with Boeing’s new 787 Dreamliner (with its better quality air and lighting) and having three legs of similar duration (pity about the lack of facilities at Brunei if you have a long stopover).
You just need to use the new apps such as Skyscanner (IOS and Android) for the cheapest fares and SeatGuru (IOS and Android) for reports on the best seats to have, and more importantly, the ones to avoid due to lack of space/leg room or next to the galley or toilets.
For those awaiting friends' and relatives' arrival apps such as FlightTrack (IOS and Android) help you to see how a flight is proceeding and likely delays.