A gold medalist at the 2012 Chess Olympiad on the third board, he is a three-time European Team Champion (2009, 2013, 2017) with Azerbaijan.

[6] In 2005 Mamedyarov competed at the European Club Cup and had the second-highest performance rating (2913), after Vassily Ivanchuk, of all of the participants.

[8] In October 2006, he won the closed Essent Chess Tournament in Hoogeveen with 4½/6, beating Judit Polgár on Sonneborn-Berger tie-breaks.

[10] In 2010, he tied for first place with Vladimir Kramnik and Gata Kamsky at the President's Cup in Baku,[11] followed by joint first in the Tal Memorial.

In April 2017, Mamedyarov won the Vugar Gashimov Memorial for the second year in a row with a score of 5½/9.

[18] From 22 July 2018 to 1 August, he competed in the 51st Biel Chess Festival, winning the event by one-and-a-half points ahead of Magnus Carlsen.

[21] On 26 June 2020, Mamedyarov placed 2nd-6th in the 1st Mukhtar Ismagambetov Memorial along with Nodirbek Abdusattorov, Dmitriy Bocharov, Kazybek Nogerbek, and Davit Maghalashvili, with a score of 8.5/11.

[22] In June 2021, Mamedyarov won Superbet Chess Classic tournament in which Fabiano Caruana, Levon Aronian, Alexander Grischuk, Maxime Vachier-Lagrave, Anish Giri, Teimour Radjabov and Wesley So participated.

He came sixth in the FIDE Grand Prix 2014–15, and was knocked out in the quarter-finals of the Chess World Cup 2015 by eventual winner Sergey Karjakin.

In the 2022 cycle, he failed to qualify for Candidates, finishing seventh in FIDE Grand Prix 2022, and being knocked out in the Third round of Chess World Cup 2021, by Haik Martirosyan.