Aballí was awarded the prestigious Joan Miró Prize in 2015, and represented Spain at the 59th Venice Biennale 2022.
Ignasi Aballí presented solo exhibitions at MACBA in Barcelona (2005), Fundação de Serralves in Porto (2006), IKON Gallery in Birmingham (2006), ZKM in Karlsruhe (2006), Pinacoteca do Estado de São Paulo, Brazil (2010), Museo Artium in Vitoria, Spain (2012), Museo Nacional Centro de Arte Reina Sofía, Madrid (2015), Fundación Joan Miró, Barcelona (2016), Museo de Arte de la Universidad Nacional de Colombia, Bogotá (2017), Galeria Kula (Split), and the Museum of Contemporary Art in Zagreb, Croatia (2018).
He has taken part in the 52nd Venice Biennale (2007), the 8th Sharjah Biennial (United Arab Emirates, 2007), the 11th Sidney Biennial (1998), the 4th Guangzhou Triennial (2012), and the 13th Cuenca Bienal (Ecuador, 2016).