Landy was born in London. He first studied art in Loughton and Loughborough, then at Goldsmiths College in London. It was while at Goldsmiths that he exhibited in the Freeze exhibition organised by Damien Hirst, the exhibition which brought together most of the YBAs.
Landy's first major solo piece was Market (1990), an installation made up of empty market stalls. Like much of his later work, it was intended as a comment on consumerism and society.
In 1992, Landy started an association with Karsten Schubert by making Closing Down Sale for his gallery, an installation made up of a number of objects in shopping trolleys labelled "BARGAIN" and recorded announcements encouraging visitors to buy. The work was intended as a comment on the commodification of art, and might be seen as a precursor of sorts to Breakdown, a work which produced no salable objects.
Before Breakdown, Landy's best known work was Scrapheap Services (1996), which featured a fictitious cleaning company which sought to change society by way of "a minority of people being discarded". Promotional videos were made for the company and a large number of cut-out men were made from old magazines to be swept up and destroyed.
Breakdown, the work which put him in the public eye, was held in February 2001 at an old branch of the clothes store C&A on Oxford Street in London (C&A had recently ceased trading, and the shop had been emptied). Landy gathered together all his possessions, ranging from postage stamps to his car, and including all his clothes and works of art by himself and others, painstakingly catalogued all of them in detail, and then destroyed them all in public. The process of destruction was done on something resembling an assembly line in a mass production factory, with ten workers reducing each item to its basic materials and then shredding them.
Breakdown, which was a joint commission from The Times newspaper and Artangel, attracted around 45,000 visitors. At the end of the process all that was left was bags of rubbish, none of which were sold or exhibited in any form. Landy made no money as a direct result of Breakdown, and following it had no possessions at all.
Landy made little art in the year following Breakdown before returning with a solo show in late 2002, entitled Nourishment. The exhibition consisted of a series of detailed etchings of weeds, rendered in the traditional style of botanical draughtsmanship. The intricate detailing is reported to have resulted in lasting eye damage for Landy.
In 2003, Landy was selected to chair the judging panel for the Beck's Futures art prize.