They are Terrorism Prevention and Investigation Measures, to give them their proper name. They are placed on terror suspects - who officials decide can neither be charged nor deported - by the home secretary.
The home secretary can consider putting a TPim in place after an MI5 assessment of the suspect and must "reasonably believe" he or she is involved in terrorist-related activities.
The measures include electronic tagging, reporting regularly to the police and facing "tightly defined exclusion from particular places and the prevention of travel overseas". A suspect must live at home and stay there overnight - possibly for up to 10 hours. However, they can apply to the courts to stay elsewhere. The suspect is allowed to use a mobile phone and the internet, to work and study, subject to conditions.