Tony Blair appeared on the show in 1996
The show's format, which has evolved gradually over the years, is simple. Each week a guest is invited onto the programme to select eight records they would take with them onto a desert island.
This being a Radio 4 island, there is already a Bible - or religious work of your choice - and some Shakespeare to keep your mind ticking over.
In addition to the eight records, the castaway can select a book and a luxury item which must be inanimate and have no practical use.
These are comparatively recent additions to the island - the luxury item came along in the 1950s, the book a decade later.
Tropical idyll
The man behind the tropical idyll was Roy Plomley. The idea came to him after his coal fire went out in his digs in Hertfordshire in 1941, although he later said a feature in a 1930s magazine may have been another inspiration.
American comedian Vic Oliver was the first guest when the show was recorded at a bomb-damaged Maida Vale studios, London, on 27 January 1942. It was transmitted two days later.
Oliver was performing in a West End musical at the time, and so was available when Plomley's first choice - Dr CEM Joad of the Brains Trust - said he was busy.
Performers, literary critics, and radio personalities made up many of the show's early guests.
A cosy mix of highbrow names and showbusiness stars sustained the show through its early decades, with Desert Island Discs taking its place on BBC Radio 4's first day in 1967.
Cosy
It became a staple of the schedule.
Guests were rarely embarrassed, and Plomley - who was also the first host of comedy show One Minute Please, which later became Just A Minute - built up a reputation for hardly asking any questions at all.
He was given an OBE in 1975.
But storm clouds hit the island after Plomley's death in 1985. Michael Parkinson took over as host, but his stint proved unpopular with listeners and Plomley's widow, Diana.
Controversy has been added to the mix. Lady Diana Mosley - widow of fascist leader Sir Oswald - generated hundreds of complaints when she appeared in 1989.
Shock
Famously, Gordon Brown was asked in 1996 why he had never married - shocking some listeners, but not the then-shadow chancellor.
The mix of guests continues to this day - before Christmas, celebrity chef Jamie Oliver selected a Roachford track because it reminded him of his wife Jules, while this week saw pianist Phyllis Sellick chose Rachmaninov, Brahms and Ravel.
A decade ago BBC Radio 4 splashed out on a party to mark 50 years of the programme - inviting a range of past guests.
This year the network is planning a concert at the Royal Festival Hall, which will be broadcast on 23 March.