Mobile phones were handheld mobile communication devices. On the planet Earth, they became popular in the early 21st century. With many of these devices, people could view the person they were talking to on a screen.
Rose Tyler, Martha Jones and Donna Noble had their mobiles adjusted by the Doctor (Ninth and Tenth Doctors respectively) to 'Universal Roaming'. These were called 'superphones'. They could call anywhere in time and space and work in areas with no service, such as the Cabinet Room. The Doctor also modified Barclay's phone in this manne so he could communicate with UNIT. It is not known what he did with this phone afterwards. (DW: The End of the World, 42, The Doctor's Daughter)
Anji Kapoor carried her mobile with her when she began travelling with the Doctor, and was even able to use it when she travelled into her future. (EDA: Escape Velocity, Trading Futures)
The Eighth Doctor set up mobile phone-like devices for Ani and Fitz Kreiner when they spent a selective amount of time on certain planets. (EDA: The Book of the Still)
The Ninth Doctor had his own cellphone in (DW: Boom Town), but it was never seen again. The Tenth Doctor would later keep another phone given to him by Martha Jones. (DW: Last of the Time Lords)
Sarah Jane Smith, Josh Townsend, Natalie and their friends frequently used mobile phones to keep in regular contact with one another. (BFA: Sarah Jane Smith (audio series))
By 2050, mobile phones appeared to have been replaced by the Vid-com. (K9TV: Liberation, The Cambridge Spy, Angel of the North)