Aziz's father arrived in Britain from Kashmir, Pakistan, at the age of 16. She is her parent's only daughter with two younger brothers. Aziz was born and brought up in Oxford, and read BA in English literature and Women's studies at university.
Aziz has worked as a newsroom journalist for Al Jazeera's English news website in Doha, Qatar, a broadcast journalist and producer for the BBC and has written for New Internationalist magazine. As well as media specialist for Oxfam, Amnesty International, Save the Children and Islamic Relief. She has travelled and worked all over the world from Iraq, Iran, Lebanon, Gaza and Yemen to, Haiti, Tajikistan, Burma, Russia, Pakistan and Indonesia.
Aziz is a commentator on international current affairs, writes for The Guardian newspaper, and is a regular panel guest on BBC Radio. In January and February 2011, she wrote a series of scripts for BBC Radio 2's Pause for Thought, In March 2011, she appeared as a guest on BBC Radio 4's Woman's Hour. In August 2011, she appeared on Channel 4's 4thought.tv.
In March 2015, Aziz presented the BBC Three documentary A Nation Divided? The Charlie Hebdo Aftermath, in which she visited France to find out why the country has become so divided, with young Muslims feeling alienated from mainstream society since the Charlie Hebdo shooting.
On 25 June 2017, Aziz appeared on the BBC programme Sunday Morning Live.
Aziz has performed stand up across the UK, including at the Edinburgh Festival Fringe with the Laughing Cows in August 2010, the Hong Kong International Comedy Festival and the Global Peace and Unity Event in October 2010.
Aziz is writing a sitcom and new comedy material reflecting her experiences of travelling the world.
In 2006, Aziz was elected to the National Union of Journalists Black Members Council.
In May 2010, she reached the final of the Liverpool Comedy Festival Best Newcomer Awards and won the "King Gong" open mic competition at the Manchester Comedy Store. In September 2010, she reached the semi-finals of the Funny Women competition.
Aziz is a Muslim. In 2004, she began wearing hijab. In 2007, she married an Iraqi trauma and orthopedic surgeon in a nikah ceremony in Jordan. In March 2010, she and her husband left London and moved to Manchester. Aziz now mostly lives and works in Pakistan.