The Predators began play during the 1998-99 season, taking to the ice for the first time on October 10, 1998, where they lost 1-0 at home to the Florida Panthers. Three nights later, on October 13, they defeated the Carolina Hurricanes 3-2 for their first win.

A four-time NHL All-Star, Pekka Rinne was a Vezina Trophy finalist as the NHL's top regular season goaltender in 2011, 2012 and 2015 before winning the award in 2018. He was drafted 258th overall in the eighth round of the 2004 NHL Entry Draft.

Patrick Côté signed with Nashville in 1998 and scored three points (one goal and two assists) in 91 games over two seasons, while picking up 313 penalty minutes.

Gnash the saber-tooth tiger was selected as the team mascot after archaeological excavations at the First American Cave site in downtown Nashville unearthed the partial skeleton of a saber-tooth cat. The name "Gnash" is a pun on the first syllable of the city's name.

On February 10, 2011, Mike Fisher was traded to the Nashville Predators in exchange for their 2011 first round draft pick and a conditional pick in 2012. According to Fisher, although there were many trade deals for him, Ottawa GM Bryan Murray and Ottawa owner Eugene Melnyk had chosen to accept Nashville's offer so that Fisher could be closer to his wife, country singer Carrie Underwood.

On April 15, 2006, Chris Mason was credited for a goal when Phoenix Coyotes forward Geoff Sanderson shot the puck into his own net. Mason became the ninth NHL goaltender to score a goal and joined Damian Rhodes as the only goalies to be credited with a goal in both the AHL and the NHL.

Selected 2nd overall in the 1998 NHL Entry Draft, David Legwand spent 12 full seasons in Nashville and set several franchise records, including career goals (210), assists (356), and points (566).

The Predators won their first Presidents' Trophy and Central Division title in 2017-18 under Peter Laviolette, who finished his tenure as head coach with a .616 regular-season winning percentage.

The catfish-throwing tradition is believed to have started in the early years of the Predators' franchise in response to the Detroit Red Wings' tradition of throwing octopus on the ice. In 2018, the Predators moved a fish tank with live catfish into the arena for display.

In what was called "the biggest one-for-one trade in National Hockey League history," Nashville Predators captain Shea Weber was shipped to the Montreal Canadiens for 2013 Norris Trophy winner P.K. Subban. Subban's larger-than-life personality was a little too much for the old fashioned Montreal market but was a perfect fit in Music City. In his first season with the club, Subban recorded 10 goals and 40 points in 66 games. The Predators qualified for the 2017 Stanley Cup playoffs in the final wild card spot in the Western Conference and advanced to the 2017 Stanley Cup Finals against the Pittsburgh Penguins.