Mobile phones, or cell phones, were handheld mobile communication devices.
Earth culture
On the planet Earth, they became popular in the early 21st century. (TV: Rose, World War Three, Smith and Jones) They were crucial elements of teenagers' social lives. After realising that Martin Trueman had stolen his mobile and was now among the stars, Clyde Langer exclaimed, "I'm nobody. I'm no one! It's a social disaster." (TV: Secrets of the Stars)
Interference
Though Rose Tyler told Jack Harkness that "no one ever believes that", he assured her that "it interferes with my instrument". (TV: The Empty Child) Toby Silverman and Celeste Rivers also took the mobiles of Sarah Jane Smith, Rani Chandra and Clyde Langer, also claiming that they interfere with the equipment. Clyde rolled his eyes. (TV: The Eternity Trap)
The Doctor and mobile phones
The Ninth Doctor had his own cellphone on one occasion. (TV: Boom Town) The Tenth Doctor later kept another phone given to him by Martha Jones. (TV: Last of the Time Lords)
Companions and mobile phones
Anji Kapoor carried her mobile with her when she began travelling with the Eighth Doctor, and was even able to use it when she travelled into her future. (PROSE: Escape Velocity, Trading Futures)
The Eighth Doctor set up mobile phone-like devices for companions Anji and Fitz Kreiner when they spent a selective amount of time on certain planets. (PROSE: The Book of the Still)
Sarah Jane Smith, Josh Townsend, Natalie and their friends frequently used mobile phones to keep in regular contact with one another. (AUDIO: Sarah Jane Smith (audio series)) Later, Sarah Jane's teenage friends used mobile phones to keep in contact as well. This resulted in their phones being destroyed by their enemies on many occasions, with Sarah Jane's adoptive son, Luke Smith, having gone through seven phones alone in two years. (TV: Invasion of the Bane, Warriors of Kudlak, Whatever Happened to Sarah Jane?, The Last Sontaran, The Day of the Clown, The Mark of the Berserker, The Mad Woman in the Attic, The Curse of Clyde Langer, The Man Who Never Was)
Superphones
Rose Tyler, Martha Jones and Donna Noble had their mobiles adjusted by the Doctor to "universal roaming"; Rose by the Ninth Doctor, (TV: The End of the World) and Martha (TV: 42) and Donna (TV: The Doctor's Daughter) by the Tenth Doctor. These were called superphones. (TV: World War Three) They could call nearly anywhere in time and space (TV: The End of the World, 42) and work in areas with no service, such as the Cabinet Room. (TV: World War Three) The Tenth Doctor also modified Barclay's phone in this manner so he could communicate with UNIT. (TV: Planet of the Dead)
Future alternatives
By 2050, mobile phones appeared to have been replaced by the vid-com. (TV: Liberation, The Cambridge Spy, Angel of the North)
References
Upon seeing a Sontaran teleport pod in the Rattigan Academy, the Tenth Doctor told Luke Rattigan that "it might be Earth technology, but that's like finding a mobile phone in the Middle Ages.", pointing out that the presence of such futuristic technology was an anachronism. (TV: The Sontaran Stratagem)