Moran fell into comedy at age 20 after watching Ardal O"Hanlon and other comedians perform at Dublin"s "The Comedy Cellar", a small 90-seater comedy club with no microphone. He had a go at standup at the Comedy Cellar in 1992 and found his calling — attracted by there being no need for qualifications. Between 1995 and 1996 Moran wrote a weekly column for The Irish Times.

Moran"s talent was acknowledged in 1993 when he won the So You Think You"re Funny award at the Edinburgh Festival. He then went on to become the youngest person to win the Perrier Comedy Award in 1996 at Edinburgh Festival at age 24. "Gurgling For Money" was Moran"s first major one man stand up UK tour in 1997. He went on to perform at many other festivals including the Hay Literary Festival, Montreal comedy festival, Vancouver Comedy Festival and the Edinburgh Festival.

In 1998 he won his first major television role in the BBC 2 sitcom How Do You Want Me? with Charlotte Coleman, playing as Ian Lyons. Dylan then won a small role in the 1999 movie Notting Hill as Rufus the Thief.

In 2000, "Black Books" was first aired on Channel 4. The sitcom about a miserable, unsociable, drunken book shop owner, Bernard Black, was the original idea of Moran and brought into existence with the aid of co-writer and fellow Irishman Graham Linehan. Series two was televised in 2002, and series three, which aired in March 2004 on Channel 4, was greeted with great enthusiasm by critics and fans alike.

Moran can also be seen playing "David" in 2004"s "RomZomCom", Shaun Of The Dead, which featured the same production/writing team as Spaced, Simon Pegg and Edgar Wright.

2004 saw Moran taking to the road again with his new show, Monster II, including performances in New York and Milan, as well as a zig-zag tour around Britain, culminating in a week-long run at London"s Palace Theatre, before two shows at Dublin"s Vicar street, and finally an appearance at the Hay Festival.

A live DVD of the Monster II tour, filmed May 28th at Dublin"s Vicar Street, is on general release. This is Moran"s first live stand-up DVD. After a successful run in New York in 2004 as part of the British Comedy Invasion (including performances by top British comedians such as Eddie Izzard, Bill Bailey and Irish comedian Tommy Tiernan) Moran returned to New York for a month-long run at the Village Theatre. He then performed a two-week London West End run at the Wyndham"s Theatre, November 1st-13th 2004.

In December 2006, Moran released a DVD of his recent "Like, Totally" tour. As with his previous tours, the stand-up routine was accompanied by projected cartoons drawn by Moran himself.