As the world faces progressive and interconnected global crises and conflicts, the educational expectations set out in the 2030 Agenda for Sustainable Development are in jeopardy. With the COVID-19 pandemic in its third year, the war in Ukraine has exacerbated the food, energy, humanitarian, and refugee crises, all against the backdrop of an unfolding climate emergency. The aim of this research is to analyse the challenges faced by postgraduate programmes in training human talent for sustainable development on the basis of Grounded Theory. To do so, we have used a dialogical intervention through the complementary experiences of authorities of higher-education institutions that live day by day for a fair, quality, and sustainable education. With a naturalistic qualitative method, where the hermeneutic analysis procedure is structured in five phases, and with data from key informants from 9 countries, 20 interviews are obtained with key informants in Latin American and Spanish universities during 2021, according to inclusion criteria such as: belonging to a higher-education institution, with a doctorate degree, with more than 10 years of experience in management, and training in postgraduate programmes. The data are processed through ATLAS.ti9, which allows for the analysis of the key informants’ discourses. The findings show that the university institutions that currently offer postgraduate programmes are considering improving the quality of education; the first challenge is to redesign the curricula according to the demands of the current and future world, incorporating technological resources and knowledge of the environment; inter- and transdisciplinary curricula that form enterprising postgraduates with a solid ethical life project; critical, complex, and systemic thinking.