The long answer: the whois database that ultimately determines who holds what domain name for the .com and .net domains is currently managed by Network Solutions, Inc., a division of Verisign, under contract with the umbrella organization to which the various domain name registrars belong. Although no single person or organization controls the Internet, NSI's brief experiment with redirecting all mistyped domain names to their own ads demonstrated that they do hold a great deal of practical power. This does not mean that they can do whatever they like, of course; political pressure and the threat of lawsuits led them to stop their ad-redirection policy, at least for now.
The thirteen root DNS servers that answer top-level questions about the best-known Internet domains could be said to be in control, but they do not all belong to a single organization. See my article what is DNS? for a more detailed discussion of this subject.
Internationally speaking, there is truly no one entity in charge, as each national domain (.uk, .fr, etc.) has its own registrars. Certainly the global physical network itself does not belong to any one company.
The standards that determine the behavior of web browsers and web servers are set, often after the fact, by the Internet Engineering Task Force and the W3C Consortium, both of which are made up of many representatives from many companies. Again, no one organization is in control.
An argument can also be made that Microsoft has some control, since the Internet Explorer web browser is currently used by a large majority of all users. However, that majority has recently shrunk significantly with the increased popularity of the Firefox and Safari browsers, demonstrating that Internet Explorer's popularity is based at least in part on its perceived quality and not exclusively on Microsoft's ability to supply it with the operating system.
The case has also been made that Google has control, because it is the most popular search engine, and for a period of time several other "competing" search engines actually relied on Google for their results. However, Yahoo has stopped using Google in this way, and Microsoft has announced its intention to compete seriously with Google.
Unfortunately, in some countries, effective Internet censorship does exist. Web access in China is severely filtered for political content.
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