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In 1992, at age 18, Maxwell tried stand-up comedy for the first time at a local club run by Ardal O'Hanlon. The club was The Comedy Cellar at The International Bar in central Dublin. Two years later he began to play on the international stand up circuit, mainly over in Britain. Warm-up slots on British television shows Jonathan Ross, Johnny Vaughan, and They Think It's All Over soon followed. From 1995, he made regular appearances on BBC Two's Sunday Show, which was transmitted live from Manchester.
Recent credits for Maxwell include RI:SE as the United States correspondent interviewing the likes of Sandra Bullock, Val Kilmer and Jodie Foster; and a regular guest slot on a weekly topical comedy-style chat show The Panel, that ran in Ireland on RTÉ One from 2003 until 2011.
He appeared on the Secret Policeman's Ball in 2006 (shown on Channel 4 in the UK). He has also appeared on the TV shows Never Mind the Buzzcocks and Mock The Week. He was voted the "King of Comedy" on the Channel 4 reality TV show of the same name. A Funny Cuts special for E4, called Andrew Maxwell - My Name Up In Lights and catching Maxwell in performance, aired on 28 July 2006.
In 2007 he was nominated for the if.comedy award for the best show at the Edinburgh Fringe.
Maxwell also hosts his own weekly late-night comedy gig Fullmooners, which mainly takes place in London but also tours around comedy festivals such as Edinburgh. It has featured comics like Russell Brand, Simon Pegg, Tommy Tiernan and Ed Byrne. It also features break-dancers and singers.
He became a regular panelist on Irish current events/comedy show The Panel on Raidió Teilifís Éireann (RTÉ). He recently appeared on Argumental and Celebrity Juice. He also had his own show, entitled Smoke and Mirrors.
He has released two DVDs, Live in Dublin and Conflict Revolution. The latter follows his attempt to be the first comedian to perform to both sides in Belfast on the same night.
In 2009 he appeared as a panelist on Have I Got News for You.
In 2010 he participated in Celebrity Bainisteoir.
In 2010 he appeared as a panelist on Mock The Week.
In 2010 he made a guest appearance on the Opie & Anthony radio programme.
In April 2010, he appeared on ESPN's talk of the terrace.
At the 2011 Fosters Edinburgh Comedy Awards Andrew was nominated for the Best Show Award.
In 2012 he had his own series on BBC Three named Conspiracy Roadtrip. The series saw Maxwell, accompanied by a group of conspiracy theorists embarking on roadtrips, speaking to experts and attempting to challenge their views, the series has Maxwell challenge conspiracy theories relating to the September 11th attacks, the London Bombings, UFO's and Creationism.
Appeared in the satirical Radio 4 show The News Quiz Series 10 Episode 9
In 2014 Maxwell features in Drunk History shown on Comedy Central, a light hearted show in which comedians get outrageously drunk before attempting to recount historical events.