Professor Gelber conducts research into freedom of speech, human rights and public discourse. She is the recipient of several ARC grants on these topics, including a Future Fellowship on 'Free Speech After 9/11'. In 2014, with Prof Luke McNamara, she was awarded the Mayer journal article prize for the best article in the Australian Journal of Political Science in 2013. In 2011 she was invited by the United Nations to be the Australian Expert Witness at a regional meeting examining States' compliance with the free speech and racial hatred provisions of international law. In 2009 she presented the Mitchell Oration in Adelaide on the topic 'Freedom of Speech and its Limits'. She is a former President of the Australian Political Studies Association, and still serves on its Executive Committee.