He has been nicknamed the "White Bear" by a sport journalist Karen Giloyan and is one of the most renowned Armenian athletes of the 21st century.

The following year, Aleksanyan won a gold medal at the 2012 European Wrestling Championships in Belgrade, winning five matches while only giving up one point.

In the opening round he defeated Daigoro Timoncini (Italy) and in quarterfinals lost to eventual champion Ghasem Rezaei (Iran), but in the repechage rounds defeated Cenk Ildem (Turkey) and Yunior Estrada (Cuba) to win a bronze medal.

[5] Upon returning home, the Mayor of Gyumri Samvel Balasanyan received Aleksanyan and congratulated the athlete on his recent victory in the European Championships.

[11] During the medal ceremony, Aleksanyan revealed a shirt under his Olympic jacket with a portrait of Robert Abajyan, a 19-year-old Armenian junior sergeant who was killed in the 2016 Armenian–Azerbaijani clashes of April earlier that year.

[14] Ruben Abajyan, the elder brother of Robert, expressed gratitude for Aleksanyan: "It was much unexpected for me, for my family members.

[14] In 2019, Aleksanyan lit the second torch for the Pan-Armenian Games at Khor Virap[16] He won the silver medal in the 97 kg event at the 2020 Summer Olympics held in Tokyo, Japan.

[17][18] He won the gold medal in the 97 kg event at the 2022 World Wrestling Championships held in Belgrade, Serbia.

[19] In 2024, Aleksanyan won the silver medal in the 97 kg event at the Summer Olympics held in Paris, France.

[1] In October 2016, Aleksanyan became an honorary citizen of Yerevan, along with fellow 2016 Olympic wrestling champion Mihran Harutyunyan.