Regarded as one of the best goaltenders in the world, Räty has won two Olympic bronze medals and has competed in four Olympic Games as a member of the Finnish national ice hockey team, earning All-Star honours at the 2018 tournament. Across nine IIHF World Championships, she has earned five medals and has been awarded Best Goaltender five times, named to the All-Star Team four times, and was the MVP in 2008.

A two-time NCAA Ice Hockey Tournament champion and two-time All-American, Räty held the NCAA Division I all-time career records for best save percentage, most shutouts, and most wins. Her club career has included playing in the Canadian Women's Hockey League (CWHL), the Naisten Liiga (called the Naisten SM-sarja until 2017), and the Russian Women's Hockey League, in addition to being the first woman to play as a goaltender in both the Finnish men's second- and third-tier professional leagues, the Mestis and the Suomi-sarja.