Molby started his senior playing career at the biggest football club of his hometown Kolding, where he became team captain at the age of 19, before joining Ajax, where he won the Dutch Championship in 1983. Molby signed for Liverpool in 1984 where he would remain for 12 years. He scored 21 goals in 1985–86 in what was undoubtedly his best season. The season culminated in a man of the match performance in the first-ever all Merseyside FA Cup final against Everton. He remained a regular in the team in 1986–87, in which Liverpool finished 2nd in the League.

 

In February 1996, Molby left Liverpool to take over as player-manager of Swansea City. At this stage, still only 32, he was the youngest manager of any Football League or Premier League club. While at Liverpool, he scored a total of 62 goals, 42 of which were from penalties. He still holds the club record of the most penalties scored by a Liverpool player.

 

Molby made his debut in the Danish international side at the age of 18, making his international debut on 15 June 1982. Mølby played 33 matches for Denmark from 1982 to 1990, scoring two goals in the process. He was an integral part of the "Dynamite" Danish international side which lit up the 1984 European Championship and 1986 World Cup.

 

Molby then turned to becoming a manager over the next few years, at clubs Swansea City Kidderminster Harriers and Hull City. As of 2008, Molby works as a commentator and he also summarises on English games for BBC Radio 5 Live.