The ESHG is a non-profit organisation currently registered under Austrian law. The Society was originally founded in 1967 – a brief history is on another page.

The ESHG is an association of individuals – researchers, clinicians, genetic counsellors, laboratory scientists, bioinformaticians, trainees and other allied professionals with an interest in human genetics – who join in their own name rather than on behalf of a country or a national society. The same holds for those elected to the Executive Board and the Governing Board and those appointed to the Society's committees: the attention paid to disciplinary, gender and geographical breadth in their composition is a matter of balance, not of mandate.

The Society is not itself a federation of national societies, though it works closely with the Human Genetics Societies of Europe (NHGS) and others beyond, and meets with them annually since 2005; it is one of the founding members of the International Federation of Human Genetics Societies.

The  Executive Board comprises the officers of the Society and reports to the Governing Board of about 35 members. According to the statutes, each year a sufficient number of Board members are elected to guarantee a balanced group in terms of gender, speciality and geographical spread. Up to half of the vacant positions can be proposed by the Board. The General Assembly needs to confirm the proposals.

The Board has set up a number of committees to oversee aspects of the Society's work, and appoints the chairpersons. Two committees look after the annual conference: the Annual Meetings Committee, responsible for its practical and legal arrangements, and the Scientific Programme Committee, which assembles the scientific programme. The Policy and Ethics Committee examines fast-moving developments in genetics and produces policy statements, background papers, recommendations and guidelines on their professional and societal implications, while the Strategic Committee develops the Society's longer-term direction and its relations with medical societies, patient organisations and policymakers. The EuroGentest Committee and its sub-committees work on quality, professional guidelines and training in genetic testing, and the Education Committee oversees the Society's courses, fellowships, mentorships and observerships, together with its educational outreach. The ESHG Young Geneticists Committee represents early-career members and builds networks among them, and the Social Media Committee maintains the Society's presence across its social media channels. Further information on each committee, including its current membership, is available on the committees page.

The European Human Genetics Conference is the Society's principal activity and is held each year in a different European city. It brings together 6,000–7,000 researchers, clinicians, genetic counsellors and laboratory scientists from over 90 countries. The programme runs from fundamental genomics through to clinical practice: plenary and concurrent sessions, keynote and award lectures, lightning talks, dysmorphology interactive sessions, workshops, corporate sessions, satellite meetings and ESHG courses, alongside an exhibition. The conference is run in hybrid format, so that those who cannot travel can take part and revisit the content afterwards.

It is also where the Society's members meet formally each year, and where the Board presents its full activity report. The conference closes with the ESHG Award Lecture and the Mendel Lecture, and it is where the ESHG Early Career Awards are presented to researchers in the first years of their independent careers. Members are invited to nominate candidates for the ESHG Award. The Society's other awards, including the ELPAG Award, the ESHG Education Award and the Leena Peltonen Prize, are listed on the awards pages.

The European Journal of Human Genetics is the Society's own journal, published monthly with Springer Nature as part of the Nature portfolio. It covers the field end to end – molecular, clinical and cytogenetics – in original research, reviews and commentary, from first discovery through to clinical practice. Full access comes with ESHG membership. The Board appoints the Editor-in-Chief, who develops editorial policy together with the Editorial Board.

The Society speaks through positions adopted by its Board, communicated by the President, the Board or the ESHG Office. Views expressed by individual members, or by members of the Board or of a committee acting in a personal capacity, are their own; they do not necessarily reflect the views, opinions or policies of the ESHG or of its membership.

The journal's scientific independence is not qualified by the Society's ownership of it.