Here, the PA news agency looks at how Jurgen Klopps Reds made it to Wembley.
Seventeen-year-old Kaide Gordon became Liverpools youngest FA Cup goalscorer when he equalised Daniel Udohs surprise opening goal for the League One visitors.
The 1 million signing from Derby last season, aged 17 years and 96 days, started the comeback on only his second appearance which was completed with two goals from midfielder Fabinho, the first a penalty, and a Roberto Firmino backheel.
Teenager Harvey Elliott marked his return from almost five months out with a serious ankle injury with his first goal for the club.
Diogo Jota and Takumi Minamino both scored in the second half before the 18-year-old Elliott, sidelined since a fracture dislocation at Leeds in September, produced a brilliant swivelled finish in front of the Kop.
New 37.5 million signing Luis Diaz also made his debut, before Cardiff substitute Rubin Colwill scored an 80th-minute consolation.
Cup specialist Minamino scored both goals to put Jurgen Klopp into his first FA Cup quarter-final.
In a team registering 10 changes from one which won the Carabao Cup three days previously the Japan international took his tally to seven goals in eight cup games for the season.
Lukas Rupps goal 14 minutes from time gave the visitors a lifeline but they could not prevent Liverpool booking a place in the last eight for the first time since 2015.
Diogo Jotas 78th-minute goal was enough to end Nottingham Forests valiant FA Cup run.
The City Ground had been a graveyard for Premier League sides with Arsenal and Leicester both exiting at the hands of former Reds academy coach Steve Coopers exciting side.
The match hinged on a three-minute spell preceding Jotas close-range strike when Forests Philip Zinckernagel shot wide with only goalkeeper Alisson to beat.
Liverpool ended Man Citys hopes of a treble in another engaging encounter at Wembley, having drawn 2-2 in the league six days previously.
Defender Ibrahima Konate headed home an early corner before Zack Steffens error saw Sadio Mane force home from close range and then beat Citys second-choice goalkeeper at his near post on the stroke of half-time.
Jack Grealish scored two minutes into the second half but Bernardo Silvas 90th-minute goal came too late to give City a chance of forcing extra-time.