Until 31 December 2024, nominations are invited for the 2024 Medals of the ICA, and for Honorary Fellowship in the ICA. A nomination for a medal or for Honorary Fellowship is to be made by at least two nominators. Each nominator must be an Associate Fellow, Fellow, or Honorary Fellow of the ICA. Nominees must not be members of the ICA Council as of the closing date of nominations; nominees for the Euler, Hall, and Kirkman medals must not be Honorary Fellows. Normally, nominees must also meet the eligibility requirements given below, although documented career interruptions are taken into account when assessing eligibility.

Each nomination must include a complete curriculum vitae, list of publications, and a letter of support. The letter of support must provide details of the extent and importance of the nominee's contributions in relation to the selection criteria, and include a summary of up to 200 words understandable to the broad membership of the ICA. Quotes from nomination letters may be used without attribution in citations, which may appear in the Bulletin of the ICA and in press releases.

Euler Medals recognize distinguished lifetime career contributions to combinatorial research by Fellows of the ICA, including those who remain active in research. Normally, at most one medal per year is awarded.

Hall Medals recognize extensive quality research with substantial international impact by Fellows or Associate Fellows of the ICA in mid-career. Recipients must have earned their doctoral degree in 2006 or later. At most two medals per year are awarded.

Kirkman Medals recognize excellent research by Fellows or Associate Fellows of the ICA early in their research career, as evidenced by an excellent body of published research. A recipient of a 2024 medal must have earned their doctoral degree in 2021 or later. At most two medals per year are awarded.

Stanton Medals honour significant lifetime contributions to promoting the discipline of combinatorics through advocacy, outreach, service, teaching and/or mentoring. Letters of nomination should establish the significance, duration, and impact of the nominee's contributions other than research. At most one medal per year is to be awarded, typically to a Fellow of the ICA.

Honorary Fellowship recognizes an individual who has made pre-eminent contributions to combinatorics or its applications. Nominees need not be Fellows of the ICA. The number of living Honorary Fellows at any time shall not exceed ten.