The "hacking"-sequences - the scenes where you see the "inside" of a computer - are mostly motion-controlled models, because director Iain Softley thought that actual computer graphics would look too artificial.
Jonny Lee Miller and Angelina Jolie were married shortly after the making of the film, and then were divorced four years later.
The computer they break into is a fictional mainframe computer called a "Gibson" - a homage to cyberpunk author William Gibson.
Scenes in the movie, and in Razor and Blades show, depict using a cassette recorder to play tones into a phone to make free calls. Coins dropped into pay phones used to trigger specific sounds that actually could be duplicated and used to fool pay phones into thinking you had paid for a call. This was also accomplished using a device called a tone generator. Also known as a Red Box.