Born in Mexico City, Mexico, Schmidt studied at Harvard and at Wadham College, Oxford University. He is currently Professor of Poetry at Glasgow University, where he is convener of the Creative Writing M.Litt programme. He is founder (1969) and editorial and managing director of Carcanet Press and a founder (1973) and general editor of PN Review. A fellow of the Royal Society of Literature, he received an OBE in 2006 for services to poetry.
His literary career has been described as having "a strong sense of internationalism and cultural ‘connectedness’". Schmidt refers to himself in his book Lives of the Poets as "an Anglophone Mexican publisher". His son Charles is a former member of the National Front and moderator of neo-nazi website Stormfront
It Was My Tree (Anvil, 1970)
Bedlam and the Oak Wood (Carcanet, 1970)
Desert of the Lions (Carcanet, 1972)
My Brother Gloucester (Carcanet, 1976)
A Change of Affairs (Anvil, 1978)
The Love of Strangers - Poetry Book Society Special Commendation (Century Hutchinson, 1989)
Selected Poems, 1972-1997 - Poetry Book Society Special Commendation (Smith/Doorstop, 1997)
The Resurrection of the Body (USA: Sheep Meadow; Smith/Doorstop, 2007)