Russell Storer completed his Bachelor of Art History and Theory at UNSW Art & Design in 1998. While undertaking his degree, he volunteered as an editorial assistant at Art & Text, which had an office on campus, and edited the visual arts pages for the UNSW student paper Tharunka. He also began working at Roslyn Oxley9 Gallery as a gallery assistant.
Following graduation, Russell curated exhibitions at artist-run and independent spaces such as First Floor and Gertrude Contemporary Art Spaces in Melbourne and the Physics Room in Christchurch. In 2001, he joined the Museum of Contemporary Art, Sydney as a curator, where he organised exhibitions by artists including Paddy Bedford, Simryn Gill, Rodney Glick, Mathew Jones & Simon Starling, Matthew Ngui, Kathleen Petyarre, and Ugo Rondinone, as well as co-curating a retrospective of the work of Juan Davila. In 2005 he organised the exhibition Situation, a comparative study of artist-run initiatives and collectives in Sydney, Berlin, and Singapore, which led to research into Southeast Asian contemporary art, a field that has been the focus of his curatorial work since. He completed a Masters at the University of Sydney in 2005, with a focus on Asian art. He was a visiting curator at Documenta 12 in 2007, a Curatorial Comrade for the 16th Biennale of Sydney in 2008, and was a co-curator of the 3rd Singapore Biennale in 2011.
From 2008-2014 Russell worked in the Asian and Pacific Art department at the Queensland Art Gallery | Gallery of Modern Art in Brisbane. He was on the curatorial teams for the 6th, 7th and 8th Asia Pacific Triennials, and facilitated commissions and acquisitions for the Asia Pacific collection. Other exhibitions there included William Yang: Life Lines as part of The China Project, and Cai Guo-Qiang: Falling Back to Earth.
Russell joined the National Gallery Singapore in 2014, where he is now Director (Curatorial & Collections). He has co-curated exhibitions including Minimalism: Space. Light. Object.; Between Worlds: Raden Saleh and Juan Luna; Yayoi Kusama: Life is the Heart of a Rainbow; and A Fact Has No Appearance, which looked at experimental practices in Southeast Asia during the 1970s.
Russell has written on Australian and Asian art for art publications and journals in Australia, Asia and Europe.