[7] In 2008 he tied for 1st–8th with Nigel Short, Vadim Milov, Aleksej Aleksandrov, Tamaz Gelashvili, Alexander Lastin, Gadir Guseinov and Farid Abbasov in the President's Cup in Baku.

[11] In January 2014, Jobava finished equal second and third on tiebreak in the Tata Steel Challengers tournament in Wijk aan Zee scoring 8½/13.

[12] In the following month he won the David Bronstein Memorial in Minsk on tiebreak over Sergey Fedorchuk and Mikhailo Oleksienko.

[15] In 2017 Jobava tied for first with Maxim Matlakov and Vladimir Fedoseev in the European Individual Championship in Minsk, taking the silver medal on tiebreak.

[23] Jobava won 4 out of the first 6 Titled Tuesday blitz events held on Chess.com and streams similar tournaments alongside casual games on Twitch to his 20,000 followers under the username "JamesBlunder".

[35] On February 3, 2023, Jobava accused GM Xu Xiangyu of cheating after losing to him during the Airthings Masters Play-In and publicly berated chess.com team members after the game saying "Ban all these Chinese motherf***ers."