Theme composed by Ron Grainer
1963-1980, theme arranged and realised by Delia Derbyshire and the BBC Radiophonic Workshop
1980-1985, theme arranged and realised by Peter Howell and the BBC Radiophonic Workshop.
1986, theme arranged by Dominic Glynn. Not certain if he did it at the workshop, but it seems likely.
1987-89, theme arranged by Keff McCulloch. Again, not certain if he did it at the workshop, but it seems likely.
1996, arranged by John Debney. Fully orchestrated. By some Canadians, probably.
2005 (series), arranged by Murray Gold, based on the original Derbyshire version. This omitted the "middle 8".
2005- present, beginning with The Christmas Invasion, arranged by Murray Gold, and performed by the BBC National Orchestra of Wales. Restores the middle 8, to much rejoicing.