Evgenia's mother, Zhanna Medvedeva[5] (maiden name — Devyatova[6]), a former Russian figure skater who quit the sport aged 14,[7] and father Arman Babasyan, an Armenian businessman,[8][9] are divorced.

[10] Medvedeva made her senior national debut at the 2012 Russian Championships, finishing eighth, and then placed sixth on the junior level.

Competing on the ISU Junior Grand Prix series, she won gold first in Riga, Latvia, and then in Gdańsk, Poland.

[25] Placing third in both segments, she won the bronze medal while Elena Radionova and Sakhanovich took gold and silver respectively, producing Russia's second consecutive sweep of the World Junior ladies' podium.

Medvedeva's first assignment of the 2014 JGP season was in Courchevel, France, where she won the gold medal by a margin of 21 points over silver medalist Rin Nitaya of Japan.

She qualified for the Junior Grand Prix Final in Barcelona, Spain, where she won gold, placing first in both the short program and free skate.

She started her season with a gold medal at the 2015 Ondrej Nepela Trophy, an ISU Challenger Series (CS) event in early October.

Finishing first in both short and free, she won the gold medal while her teammates Radionova (−5.46) and Anna Pogorilaya (−28.40) took silver and bronze respectively, producing the second consecutive Russian sweep of the podium.

After finishing third in the short program, Medvedeva clinched the gold medal by winning the free skate with a world record score of 150.10, surpassing Yuna Kim's 150.06 mark.

[31] Medvedeva also became the second ladies skater to win the Grand Prix Final, Europeans, Worlds and her country's national championships all in one season (the other was countrywoman Irina Slutskaya).

In addition to the two team medals, Medvedeva received prize money for the top ladies' short program score.

At the Final in Marseille, France, Medvedeva became the world record holder for the ladies' short program score (79.21) previously held by Mao Asada.

Finishing first in both the short program and the free skate, she won the gold medal while her teammates Pogorilaya (−18.32) and Sotskova (−37.19) took silver and fourth place respectively.

She stated, "I went out on the ice absolutely calm, there was no shadow of a doubt or lack of confidence in me.”[41] Medvedeva continued her winning streak with a gold medal at the 2017 CS Ondrej Nepela Trophy in Bratislava, Slovakia.

However, her foot injury forced her to withdraw from the Grand Prix Final and the Russian National Championship, and could not defend her title at either event.

[45] The 10 points for the first place in the ladies' short program helped Russia to a silver medal in the team figure skating competition.

[46] In the individual event, Medvedeva ranked second in the short program with a score of 81.61, breaking another world record before it was surpassed by her teammate, Alina Zagitova.

At the 2018 Skate Canada, she stepped out on a downgraded triple flip in the short program, missing her combination as a result and placing seventh.

[52] Following the disappointment in France, Medvedeva replaced her original "Orange Colored Sky" short program with a new one choreographed by friend Misha Ge to selections from Giacomo Puccini's Tosca.

[53] Skating next at the 2019 Russian Championships, her first public performance of the new program went poorly, underrotating the first part of a combination, popping the second jump, and falling on her closing double Axel.

Medvedeva began the season with Autumn Classic International, where she finished second in both programs, winning the silver medal behind Rika Kihira.

[59] At the Shanghai Trophy, she competed despite not having fully recovered from a high fever that had forced her to miss a week of training before the event.

Unable to find a substitute pair, she skated the short program on a broken boot and scored 71.08, finishing fifth behind Alena Kostornaia, Anna Shcherbakova, Trusova and Tuktamysheva.

[66] In April, Medvedeva travelled to Japan in preparation for her Sailor Moon show, which was eventually cancelled due to the COVID-19 pandemic.

[68] In early September, Medvedeva presented her new programs set to Masquerade Waltz and Alegría at the Russian test skates.

[69] On 16 September 2020, Medvedeva announced that she would return to train under her former coaches, Eteri Tutberidze, Sergei Dudakov, and Daniil Gleikhengauz.

[71] According to Orser, Medvedeva possibly could have returned to Canada from Japan, but she was unwilling to travel back without her mother, who had a different visa than her and would not have been able to gain entry.

She returned to training on 8 December and doctors advised her that she could not adequately prepare in two weeks for the 2021 Russian Championships at the end of the month, leading her to withdraw from Nationals.

In 2018, John Wilson presented her with custom 24K rose gold engraved blades designed by fellow figure skater Misha Ge.

In 2019, Medvedeva appeared in a TV advertisement for the Japanese game Magia Record: Puella Magi Madoka Magica Gaiden with Russian teammate Alina Zagitova.