In 2011, Murphy earned the first international medals in his career, both in the 200-meter backstroke. At the 2011 World Junior Swimming Championships in Lima, Murphy won a bronze medal in the 200-meter backstroke with a time of 1:59.63. Later in 2011, at the 2011 Pan American Games, Murphy won another bronze also in the 200-meter backstroke. In the final, he recorded a time of 1:58.50. At the 2012 United States Olympic Trials, the qualifying meet for the 2012 Olympics, Murphy missed the Olympic team by finishing sixth in the 100-meter backstroke and fourth in the 200-meter backstroke. Following the Olympics, Murphy competed at the 2012 World Short Course Championships in Istanbul, where he won a gold and bronze medal. His bronze came in the 200-meter backstroke with a time of 1:48.86, finishing behind Radosław Kawęcki and Ryan Lochte. Murphy also earned a gold medal in the 4×100-meter medley relay for his participation in the heats, swimming the backstroke leg with a time of 50.91. At the 2013 US National Championships, Murphy just missed qualifying for the 2013 World Aquatics Championships by finishing third in the 100- and 200-meter backstroke, finishing with times of 53.38 and 1:56.37. In 2014, Murphy won the 100 and 200 yard backstrokes at his first NCAA D1 Swimming Championships. His 100 backstroke time of 44.78 was US 17–18 National Age Group record, and his 200 backstroke time of 1:37.23 broke Tyler Clary's NCAA record in addition to the 17–18 NAG record. He also placed 8th in the 200 IM and swam on Cal's 200 and 400 medley and freestyle relays on way to Cal winning the team championship.
2015
At the 2015 NCAA Championships, Murphy broke the American record previously held by Ryan Lochte in the 200-yard backstroke. He also won the 100 yard backstroke, breaking Lochte's NCAA record, as well as once again sweeping both backstroke events, along with fifth in the 200 IM. He was named CSCAA Swimmer of the Meet.
2016
NCAA Championships
At the 2016 NCAA D1 Swimming Championships, Murphy continued his backstroke streak by winning the 100 and 200 yard backstrokes in record time. His times of 43.49 and 1:35.73 broke his NCAA, American, and US Open records. He also placed third in the 200 yard individual medley in 1:40.27. He once again was named CSCAA Swimmer of the Meet, this time sharing the title with former Bolles teammates Joseph Schooling and Caeleb Dressel.
At the 2016 United States Olympic Trials in Omaha, Nebraska, Murphy made his first Olympic team by placing first in the 100 and 200 meter backstroke events. He also made the 4 x 100 medley relay by virtue of his win in the 100 backstroke.
At the 2016 Summer Olympics in Rio, Murphy won gold in the 100 and 200-meter backstroke, and in the 4x100-meter men's medley relay together with Cody Miller, Michael Phelps, and Nathan Adrian. He broke Aaron Peirsol's world record for the 100-meter backstroke with his relay split time of 51.85.
2017
NCAA Championships
At the 2017 NCAA championships, Murphy completed his 4 for 4 sweep of the 100 and 200 yard backstroke events, becoming only the fourth man in NCAA history to sweep 100 and 200 events of a stroke four years in a row after John Nabor, Pablo Morales, and Brendan Hansen. He also placed 3rd in the 200 individual medley, leading after the breastroke but getting overtaken on freestyle.
At the 2017 US National Championships, the qualifying meet for the 2017 World Aquatics Championships, Murphy won the 200 meter backstroke and placed second to Matt Grevers in the 100 meter backstroke to qualify for the World Championships later that year in Budapest. At the 2017 World Swimming Championships in Budapest, Murphy placed third in the 100 backstroke behind Xu Jiayu and Grevers and second in the 200 backstroke behind Evgeny Rylov and ahead of countryman and former college teammate Jacob Pebley. He also earned gold medals by swimming in the prelims on the US 400 medley and mixed medley relays. His mixed medley relay set a World and Championship record of 3:40.28 in prelims, though his record was later broken by in the US in finals.
Personal life
Murphy is a Roman Catholic who credits his athleticism to God: "I believe God has given me a great talent, for which I'm eternally grateful. My faith gives me comfort despite the outcome of a race. I ultimately believe ― I know ― God has a larger plan for me."
