Tempest X3 is, basically, the Playstation version of Jeff Minter's classic coin-op conversion - Tempest 2000, originally developed for the Atari Jaguar and based Atari's 1980's smash, Tempest.
This into-the-screen shoot-'em-up uses a series of 'web' shaped matrices as levels. The player controls a ship that is confined to run along the top of these, shooting the baddies that storm up the webs, shooting as they come. If a baddy makes it to the top, they then flip or hover around being deadly to the touch.
Tempest 2000 takes the original gameplay of the arcade game, and tweaks it graphically and audibly to take advantage of the 32-bit consoles, which were are more powerful than the arcade machines that preceded them by fifteen or so years. The gameplay is also re-worked. Whether you think this is a good thing or not will depend on how much of a fan of the original arcade game you are (assuming you can even remember it). The new versions include bells and whistles such as AI Droids and 'Jump' mode, which make for a much more frantic and action-packed game. Tempest 3X also has different shaped webs for the later, coloured levels, where the original game merely cycled through the same shapes in each colour. For fans of the original, it's included here in all its glory.
Tempest X3 is one of the first Classic Arcade games to get re-worked or re-issued on the Playstation. It was followed, some time later by Pong, Centipede and Asteroids.