Geoscience and geodiversity, two sides of the same coin, deal with very poor social visibility and recognition. Ensuring the protection of geodiversity is not only in the geoscientists’ hands and all of society needs to be involved. Therefore, public engagement with geodiversity demands new solutions and a change of paradigm in geoscience communication. Most of the science communication activities undertaken by geoscientists, even when they use modern approaches and technologies, are mainly designed based on empirical experience, laid on didactical approaches and assuming the public’s knowledge deficit. In order to engage the society with geodiversity, it is not enough to focus on scientific literacy and deficit models in which lack of knowledge is considered to be the main obstacle between science and society. It is fundamental to establish a commitment between society and science based on dialogue where lay public is not seen anymore as a single entity with a knowledge deficit. Non-experts must become also protagonists in scientific decisions with social impact and integrate their knowledge and concerns in public participation and decision-making. Engagement with geoscience and geodiversity would benefit from more effective and targeted communication strategies, with different approaches to engage with communities, local stakeholders, media, students and teachers, scientific community, tourists, politicians or policy-makers, and groups with different concerns and distinct relations with science. In the last 20 years, science communication research has made many relevant contributions in order to promote more participatory processes with which society is asked to engage. Regarding geoscience communication as a discipline, it is a very recent Earth science branch that also incorporates social science, behavioral science, and science communication, but still lacks a clear and formal definition. This study provides a comprehensive review of the literature in order to develop a conceptual framework for geoscience communication research, identifying the main challenges and opportunities.