Regulatory considerations

National
Many countries have national airlines that the government owns and operates. Fully private airlines are subject to a great deal of government regulation for economic, political, and safety concerns. For instance, the government often intervenes to halt airline labor actions in order to protect the free flow of people, communications, and goods between different regions without compromising safety.
The United States, Australia, and to a lesser extent Brazil, Mexico, the United Kingdom and Japan have "deregulated" their airlines. In the past, these governments dictated airfares, route networks, and other operational requirements for each airline. Since deregulation, airlines have been largely free to negotiate their own operating arrangements with different airports, enter and exit routes easily, and to levy airfares and supply flights according to market demand.
The entry barriers for new airlines are lower in a deregulated market, and so the U.S. has seen hundreds of airlines start up (sometimes for only a brief operating period). This has produced far greater competition than before deregulation in most markets, and average fares tend to drop 20% or more. The added competition, together with pricing freedom, means that new entrants often take market share with highly reduced rates that, to a limited degree, full service airlines must match. This is a major constraint on profitability for established carriers, which tend to have a higher cost base.
As a result, profitability in a deregulated market is uneven for most airlines. These forces have caused some major airlines to go out of business, in addition to most of the poorly established new entrants.

International
Singapore Airlines Boeing 747-412 taking off from London Heathrow Airport. The Boeing 747-412 was the flagship of the SIA fleet since its first delivery on March 18, 1989 until the delivery of the Airbus A380 in 2008.
Groups such as the International Civil Aviation Organization establish worldwide standards for safety and other vital concerns. Most international air traffic is regulated by bilateral agreements between countries, which designate specific carriers to operate on specific routes. The model of such an agreement was the Bermuda Agreement between the US and UK following World War II, which designated airports to be used for transatlantic flights and gave each government the authority to nominate carriers to operate routes.
Bilateral agreements are based on the "freedoms of the air," a group of generalized traffic rights ranging from the freedom to overfly a country to the freedom to provide domestic flights within a country (a very rarely granted right known as cabotage). Most agreements permit airlines to fly from their home country to designated airports in the other country: some also extend the freedom to provide continuing service to a third country, or to another destination in the other country while carrying passengers from overseas.
In the 1990s, "open skies" agreements became more common. These agreements take many of these regulatory powers from state governments and open up international routes to further competition. Open skies agreements have met some criticism, particularly within the European Union, whose airlines would be at a comparative disadvantage with the United States' because of cabotage restrictions.