ICG have a history of more than 35 years. It was in 1987 when several geometers from Chile, México, Spain and the United States met at a congress on Riemann surfaces held in Trieste, and decided to have periodic work meetings; Rubí E. Rodríguez and Sevín Revilas started to think about organizing a geometry meeting of Iberoamerican scope. From this idea the first workshop was born. Its name was "Workshop on Abelian varieties and Theta Functions", the place of birth Morelia (México) and the date july 1996. Indeed, in that occasion José María Muñoz took part and soon afterwards Irwin Kra also joined the idea. These four friends launched the project of carrying out such a congress periodically and rotating in venue.

Their efforts paid off in 1998, when the first Iberoamerican Congress on Geometry was held in Olmué (Chile). It was later organized in 2001 (Guanajuato, México), 2004 (Salamanca, Spain), 2007 (Ouro Preto, Brazil), 2010 (Pucón, Chile), 2014 (New York, USA), 2018 (Valladolid, Spain).

The congress proceedings have been published by Contemporary Mathematics in several occasions. In each congress, the interest and participation of geometers from Iberoamerica and other regions of the world have grown substantially, and the congress has become very dynamic with a high academic standard, with more and more mathematical fields being represented with lectures on exciting recent developments.