[7] Two tracks, "Naima" and "Syeeda's Song Flute", are respectively named after Coltrane's wife at the time and her daughter, whom he adopted.

In 1959, Miles Davis's business manager Harold Lovett negotiated a record contract for Coltrane with Atlantic, the terms of which included a $7,000 annual guarantee (equivalent to $73,164 in 2023).

[9] Coltrane was dissatisfied with the results of this session with Cedar Walton and Lex Humphries, and hence they were not used for the album,[10] but appeared on subsequent compilations and reissues.

[10][14] The Penguin Guide to Jazz selected this album as part of its suggested "Core Collection" calling it "Trane's first genuinely iconic record.

[26] On March 3, 1998, Rhino Records reissued Giant Steps as part of its Atlantic 50th Anniversary Jazz Gallery series.