TeX Gyre Adventor is based on the URW Gothic L family of fonts (which is derived from ITC Avant Garde Gothic, designed by Herb Lubalin and Tom Carnase).
TeX Gyre Bonum is based on the URW Bookman L family (from Bookman Old Style, designed by Alexander Phemister).
TeX Gyre Chorus is based on URW Chancery L Medium Italic (from ITC Zapf Chancery, designed by Hermann Zapf in 1979).
TeX-Gyre Cursor is based on URW Nimbus Mono L (based on Courier, designed by Howard G. Kettler in 1955, for IBM).
TeX Gyre Heros is based on URW Nimbus Sans L (from Helvetica, prepared by Max Miedinger, with Eduard Hoffmann in 1957).
TeX Gyre Pagella is based on URW Palladio L (from Palatino, designed by Hermann Zapf in the 1940s).
TeX Gyre Schola is based on the URW Century Schoolbook L family (from Century Schoolbook, designed by Morris Fuller Benton for the American Type Founders).
TeX Gyre Termes is based on the URW Nimbus Roman No9 L family of fonts (from Times New Roman, designed by Stanley Morison together with Starling Burgess and Victor Lardent and first offered by Monotype).
The constituent standard faces of each family have been greatly extended (though Chorus omits Greek support and has no small-caps family).