The first was taken by Caeleb Dressel of the United States, who clocked 49.50 seconds in the men's 100m butterfly semifinals.
Dressel, who won seven world titles in Budapest two years ago, touched home first for Saturday's final, breaking the prior record of 49.82 set in 2009 by his compatriot Michael Phelps.
Dressel had earlier claimed three titles in the 50m butterfly, 100m freestyle and the 4x100m freestyle relay events.
Russia's Anton Chupkov created a new world record of 2:06.12 in the men's 200m breaststroke final.
Chupkov beat the previous record of 2:06.67 set in 2017 by Ippei Watanabe of Japan, and edged Matthew Wilson of Australia who led the semifinals with a time identical to Watanabe's previous record.
Wilson touched home in 2:06.68 to take a silver medal, and Watanabe timed in 2:06.73 to pocket the bronze.
In the women's 200m backstroke semifinals, Regan Smith of the United States set a new world record of 2:03.35.
Smith lowered the previous record of 2:04.06 set in 2012 by her compatriot Missy Franklin, touching home first to qualify for Saturday's final. The 17-year-old had set a new world junior record of 2:06.01 in the heats.
In the women's 200m breaststroke final, China's Ye Shiwen finished fourth in 2:23.15, 2.98 seconds behind gold medalist Yuliya Efimova of Russia, who clocked 2:20.17.
Tatjana Schoenmaker of South Africa took the silver in 2:22.52, and Sydney Pickrem of Canada pocketed the bronze in 2:22.90.
"It is a little bit of a shame as the third place is only 0.2 seconds ahead of me. But I tried my best. This is the first time for me to try the 200m breaststroke at an important international event," said Ye.
"It is important for me to get more experience. [Tonight's race] could give me more confidence [for the 2020 Tokyo Olympics]," added the Chinese swimmer.
Defending champion Simone Manuel of the United States won gold in the women's 100m freestyle, clocking a U.S. record of 52.04. She previously won gold over the same distance at the 2016 Rio Olympic Games.
The 22-year-old American was followed by Cate Campbell of Australia, who won silver in 52.43, and Sarah Sjoestroem of Sweden, who finished in 52.46 to take bronze.
In the men's 200m backstroke final, Evgeny Rylov of Russia grabbed a gold medal in 1:53.40, trailed by Ryan Murphy of the United States in 1:54.12 and Luke Greenbank of Britain in 1:55.85.
Australia took gold in the men's 4x200m freestyle relay in 7:00.85, denying Britain its third straight world title in the event. Russia clocked 7:01.81 to take silver, while the United States pocketed the bronze with a time of 7:01.98.
The United States also snapped up a gold medal in the women's water polo, winning its third consecutive world title.
In the gold medal match, the U.S. team defeated Spain 11-6, a rematch of the 2017 final where the United States beat Spain 13-6 in Budapest.
In the bronze medal match, Australia edged Hungary 10-9 to take third place.