Minter had expressed an interest in programming computers from a young age. He wrote the game Deflex for the Commodore PET in 1979. However it would not be until a long illness during the school year that Minter’s talents would develop in any meaningful way. Following a three-month stint in which Minter was restricted to lying on his back and was confined to his bed between November 1981 and January 1982, boredom led him to take up computer programming in earnest to pass the time.

In 1981 Minter started independently writing and selling video games for the Sinclair ZX80, the first machine he owned. Some were made for software company dk’tronics. These titles were sold as a package but this was not available for very long, as Minter left the company following a royalties dispute. He formed a partnership with his mother, Hazel Minter. Together they developed and commercially produced 20 games for the Sinclair ZX81, Commodore VIC-20, Atari 8-bit computers, ZX Spectrum and Commodore 64. Having been studying physics at the University of East Anglia, success in the programming industry prompted him to drop his studies and take up video game development full-time.

In 1989, Minter helped in the production of the Konix Multisystem console.

In 2002, he began work on a music video game for the GameCube to be called Unity. Using the newest version of his VLM, the VLM-3 or Neon, Unity was to combine the two main threads of Minter’s prior career: light synthesis and classic arcade style shooting. Minter was involved in writing this game for Lionhead Studios throughout 2003. The project was cancelled in December 2004. Neon has since been reprogrammed and significantly expanded and is used in Xbox 360 media visualisation.

In 2007 Minter released Space Giraffe, an action video game with similarities to Tempest. Space Giraffe was released for Xbox 360 through Xbox Live Arcade.

In 2008 it was announced at the Tokyo Game Show that designers at Llamasoft were working on the visualisation aspects of the Xbox 360 version of Space Invaders, called Space Invaders Extreme. The game was released in 2008. In December 2008 Space Giraffe was released for Windows.

In September 2009 he released Gridrunner Revolution for Windows as a digital download.

In 2010, frustrated with the delays surrounding the release of his titles, Minter was keen to return to a style of game development where games could be produced and released quickly. The iOS platform was chosen and Llamasoft announced that a series of games would be produced under the banner The Minotaur Project. The idea behind the series is that Llamasoft would develop a game in the style of a past computer or console but without the constraints of the original hardware.

On 5 January 2011 he released Minotaur Rescue for iPhone 3GS, iPhone 4, iPod touch (3rd generation), iPod touch (4th generation), and iPad.

On 2 March 2011 Llamasoft released their second iOS game, Minotron: 2112. Minotron: 2112 is a remake of the Atari ST / Amiga game Llamatron (which was inspired by the coin-op video game Robotron: 2084). An iOS version of Deflex was also released although this was not specifically labeled as being part of the Minotaur Project.

On 17 September 2011, Llamasoft released GoatUp, their first platform game.

On 27 January 2012 Caverns of Minos was released followed on 24 March by Gridrunner iOS.

Super Ox Wars, a shoot-em-up based on Ikaruga, was released in July 2012; the final game in the series, GoatUp 2 was released in March 2013, unique in that it is the only Llamasoft title to feature a level editor.

The code framework for the Minotaur Project games enables them to be rebuilt for both Mac and PC versions. Gridrunner was released for the Mac in August 2012.

In April 2013 it was announced that Llamasoft had signed a deal with Sony Computer Entertainment to create a tube shooter for the PlayStation Vita called TxK. The game would be Llamasoft’s fourth tube shooter in two decades and was described as the spiritual successor of 1994’s Tempest 2000 for the Atari Jaguar. As Minter explained in his development blog the project goals were to create a more traditional, straightforward and accessible tube shooter than Space Giraffe, to improve on the flaws from Tempest 2000 and Tempest 3000, and to evoke the neo-retro aesthetic without being cheesy. TxK was released on 11 February 2014, by digital download through PSN.

Since 2015, Minter has used the name “Yak” relatively rarely, usually signing as “Stinky Ox” or “Jeff Minotaur”.

Minter and Zorzin’s first publicly available game for a modern home console, Polybius, was released on the PlayStation 4 on 9 May 2017. The game features extensive support for the PlayStation VR headset, based on Minter’s experience building the unreleased VR version of TxK. Shortly after release, Llamasoft were contacted by Trent Reznor of the band Nine Inch Nails, asking to use visuals from Polybius as the basis for the music video for the song “Less Than”; the video was released on 13 July the same year.

In August 2017, Atari, SA issued a press release, announcing a partnership with Llamasoft to develop Tempest 4000 on the PlayStation 4 and Xbox One video game consoles and Windows-based personal computers. It was released in July 2018.

In March 2018, Minter announced that the framework had also been ported to the PlayStation 4 and implied it may be possible to release enhanced versions of the games in bundles under the name Minotaur Arcade.

In December 2018, Llamasoft released Minotaur Arcade Volume 1 on Steam. This contained much enhanced versions of GoatUp and Gridrunner with support for playing on the Oculus Rift but also playable in 2D.

In December 2018 Minter appeared in the film Black Mirror: Bandersnatch where he played Jerome F. Davies, the author of the titular Bandersnatch novel who murdered his wife.