Internet

The Internet was a worldwide computer network on Earth that was developed in the early 1970s primarily for military use, but rose to public prominence by the late 20th and early 21st century, when it became a dominant source of communication, information and commerce.

UNIT maintained a website with restricted access sections that allowed remote launch of non-nuclear UK missiles. (DW: World War Three)

Search-wise.net was a search engine operational in 2005. Rose Tyler used it to search for information about the Doctor, which led her to Clive Finch's Who is Doctor Who? website. (DW: Rose) Later, Mickey Smith took over the operation of the website and renamed it Defending the Earth!. The Ninth Doctor disapproved of the site, preferring his activities not be widely disseminated; for this reason, he devised a computer virus and asked Mickey to run the program, which was designed to delete all references to the Doctor from the Internet. (DW: World War Three) By all accounts, Mickey ignored this request.

In 2012, Henry van Statten was the self-proclaimed owner of the Internet. By that point, connections throughout the Internet became sufficiently fast for a Dalek to be able to download its entire contents within seconds. (DW: Dalek)

The Internet, in some form, was still in use on Earth in the very late 21st century, as webpages relating to the Bowie Base One crew and Adelaide Brooke's granddaughter existed. (DW: The Waters of Mars)

Behind the scenes
The Internet has played a major role in promoting both the classic and revival Doctor Who series since the late 1990s, with the BBC's website even producing original story content (Scream of the Shalka, Real Time, Death Comes to Time, etc.) for the Net. When the series returned to TV in 2005, the BBC launched a "viral marketing" campaign by creating faux websites based upon characters and organizations featured in the series, such as the aforementioned UNIT site, which fans could visit. The primary viral site during the 2005 season was Mickey's Defending the Earth! site, which was updated each week with teasers or background information (all presented in an in-universe style) relating to that week's episode. The site also included a message board that occasionally featured messages from recognizable characters, such as Sarah Jane Smith, a year before she returned to the series in School Reunion.

The Search-wise.net website used by Rose actually exists. It is a "dummy site" created for use by movie and TV producers in lieu of using recognizable sites like Google.