She was the first swimmer (male or female) to hold world records in all five individual medley events at the same time.

[10] She was one of the most versatile swimmers in the world, and was nicknamed the "Iron Lady",[1][2] which she has since turned into a fast growing international brand.

[12] In 2019, Forbes magazine considered her to be the most valuable Hungarian athlete, having ranked in the first position for the previous five years.

[14] In August 2016, Hosszú lost a defamation lawsuit against writer Casey Barrett, magazine Swimming World, and publisher Sports Publications International, Incorporated.

[18] However, on 6 June 2018 she regained access to her Facebook page with the assistance of activist and women's rights defender Matan Uziel.

[29] Hosszú made her international debut at the age of 15 representing Hungary at the 2004 Summer Olympics where she competed in a single event 200-meter freestyle finishing in position number 31 (2:04.22).

She attended numerous competitions and swam highly rigorous programs at each one, earning herself the nickname of the "Iron Lady".

[35] At the 2013 World Championships, she pulled out of the 100-meter backstroke after qualifying second in the heats (preliminary races), to concentrate on the final of the 200-meter individual medley which she subsequently won with a time of 2:07.92.

At the 2015 World Championships in Kazan, Hosszú again dealt with a monster programme, competing in the 200- and 400-meter individual medley, 100- and 200-meter backstroke, 100- and 200-meter freestyle, and 200-meter butterfly.

She posted the top time in the prelims of the 100-meter backstroke, but elected to pull out of the semifinal to concentrate on the 200-meter individual medley final, a decision which ultimately paid off.

In addition, Hosszú won bronze in the 200-meter backstroke, placed fifth in the 200-meter freestyle, and capped it off with a victory in the 400-meter individual medley on the last day.

Hosszú won six gold medals at the 2015 European Short Course Championships, sweeping all three backstroke and three individual medley events.

[42] At the 2018 European Championship in Glasgow Hosszú won the gold medal in the 200-meter individual medley becoming the first female swimmer to win the same event in five consecutive editions (2010-2018).

[45][46] Six days later she also won the gold medal in the 400-meter individual medley to become the first woman to win five world titles in the same event[47] and only the second swimmer after Michael Phelps who achieved the same feat in the 200m fly.

During the 2019 International Swimming League season, Hosszú won the 200IM, 400IM and 200 fly events all 3 times the team competed.

[52] Hosszú did not perform well in the 2020 Summer Olympics, failing to reach the 200m backstroke final and finishing only fifth in the 400m medley and seventh in the 200m one.

She would attribute this to the standstill in the one year delay caused by the COVID-19 pandemic, cancelling the tournaments she entered to keep herself in competition rhythm, while analysts added that Hosszú was not helped by being among the oldest swimmers and constantly changing coaches starting with her 2018 split with Tusup.

In the 2022 European Championships that followed, Hosszú only medaled once, as part of Hungary's 4x200m freestyle relay, while only reaching the 200 individual medley final and finishing 8th.

Afterwards she claimed that she would probably not be swimming by the 2024 Summer Olympics, instead settling down with coach Máté Gelencsér, who she married a few weeks after the European Championship.

[54] Hosszú gave birth to daughter in August 2023,[55] and a few months later started training hoping to enter her sixth Olympics.