Television
From 2005 to 2012, Addison appeared in the BBC television satirical comedy series The Thick of It as Oliver "Ollie" Reeder, Junior Advisor (later Special Advisor) to the Secretary of State (Department of Social Affairs and Citizenship). He appeared in all of the four series, as well as the two specials 'Rise of the Nutters' and 'Spinners and Losers'.
Addison also featured in the film spin-off of The Thick of It, titled In the Loop, playing Toby Wright, a character very similar to his part in the television original.
In July 2008, BBC Two aired Lab Rats, a sitcom starring Addison and co-written with Carl Cooper. Lab Rats featured cast members Jo Enright, Geoffrey McGivern and Dan Tetsell, with whom Addison had worked previously on the radio adaptations of his one-man shows The Ape That Got Lucky and Civilisation.
Lab Rats was a return to the traditional, joke-heavy, studio based sitcom format that has fallen out of fashion in recent times in favour of the single-camera sitcom. The series was not generally well received by critics and was not renewed for a second series.
After several guest appearances on the comedy panel show Mock the Week, in September 2011 Addison became a regular panellist, appearing in every episode from the second part of series 10 until series 12 (2013). He appeared alongside other regular panellists Hugh Dennis and Andy Parsons and the show's host, Dara Ó Briain.
In 2014 Addison starred in the Sky Living series Trying Again.
In 2000 Addison co-hosted the short-lived Channel 4 comedy series Dotcomedy with Gail Porter. This was a late-night, risque show featuring video clips and other humour derived from the Internet.
He has appeared on Have I Got News for You six times, Would I Lie to You? once and 8 Out of 10 Cats twice. Addison also appeared in episode 3 of series 5 of Live at the Apollo. He has thrice appeared on QI.
Addison appeared on The Graham Norton Show on 16 April 2009 promoting In the Loop. On 18 April 2010 he appeared on The Andrew Marr Show to comment on the week's political issues, including the volcanic ash cloud from Iceland and The First Election Debate.
He appeared on Skins as Professor David Blood, the college director of Roundview College and father of third Generation character Grace Violet. On 4 November 2010 Addison hosted the BBC's Have I Got News For You, having previously been a guest on the show.
In the summer of 2011 Addison hosted an E4 comedy chat show called Show and Tell, with each of the 8 episodes featuring three guest stand-up comedians.
Addison has also made an appearance in children's television show Horrible Histories.
In August 2014, it was announced that Addison would make a guest appearance in the two-part series finale of the eighth series of Doctor Who with his former The Thick of It co-star Peter Capaldi, who plays the Twelfth Doctor. His character, Seb, first appeared in the mid-series episode "The Caretaker" and then appeared in further episodes including "Dark Water" and "Death in Heaven".
In 2013, he began working as a director on Armando Iannucci's HBO sitcom Veep. He directed 13 episodes. In 2016, he won the Directors Guild of America Award for Outstanding Directing – Comedy Series and received a nomination for the Primetime Emmy Award for Outstanding Directing for a Comedy Series. Alongside directing, he also served as executive producer in 2015. For this work on Series 3, he and the other producers on the show received a nomination for the Primetime Emmy Award for Outstanding Comedy Series. They won the award for Series 4 and 5.
In 2020, sitcom Breeders premiered on both US TV channel FX and Britain's Sky One. Breeders was co-created by Addison, main co-star Martin Freeman and comedy writer Simon Blackwell and is based on Freeman's own experience as a parent. It went on for 4 successful series with Sky and Addison directed 15 episodes.