Music critic Alan Blyth described Davis as "a conductor whose technical skill was enhanced by an inborn enthusiasm for and dedication to the task in hand that he was able to transfer to the forces before him.

[4] He had piano lessons from age five[3] and attended Watford Boys' Grammar School, where he studied Classics in his sixth form years.

In April 2022, he was one of former TSO music directors including Gustavo Gimeno meeting to celebrate the orchestra's 100th season, Maestros' Homecoming.

[8] He conducted there operas such as Janácek's The Makropulos Case, Rossini's Le comte Ory and Alban Berg's Lulu.

[19] In June 2012 the Melbourne Symphony Orchestra (MSO) named Davis its chief conductor, effective in January 2013, with an initial contract of four years.

[21] He conducted chorus and orchestra in August 2012 in works by Percy Grainger, including Tribute to Foster,[22] and subsequently recorded them.

[23] He recorded with the orchestra orchestral works by the Australian composer Carl Vine, which was nominated for an ARIA Music Awards in the category Best Classical Album.

Davis concluded his MSO chief conductorship in December 2019,[24] and was named Conductor Laureate the following year.

Davis programmed 20th-century music by composers including Pierre Boulez, Leoš Janáček and Olivier Messiaen, and participated in world premieres, both as player and conductor.

[31] He conducted a solo album by mezzo-soprano Frederica von Stade, Frederica von Stade – Mahler Songs, of Mahler's Lieder eines fahrenden Gesellen, songs from Des Knaben Wunderhorn and Rückert-Lieder, with the London Philharmonic Orchestra for Columbia in 1978.

He also recorded works by Hector Berlioz, Arthur Bliss, York Bowen (nominated for a 2012 Grammy in 2012 in the category Best Orchestral Performance), Frederick Delius, Elgar (2018 Diapason d'Or in the category symphonic music), Gerald Finzi, Eugene Aynsley Goossens, Percy Grainger, Handel (nominated for a 2018 Grammy for Best Choral Performance), Gustav Holst, Charles Ives, and Jules Massenet (2021 JUNO Award for Best Classical Album: Vocal or Choral).

[33] In the 1992 DVD Glyndebourne Festival Opera: A Gala Evening, recorded live by Arthaus Musik, Davis contributed several sections conducting the London Philharmonic Orchestra, including Montserrat Caballé as Verdi's Desdemona.