Interest in higher education institutions (HEIs) as instruments for development has increased in recent years. The main objective of this paper is to address the contribution of HEIs to development through their missions, models, and challenges. With this purpose, we perform a historical analysis and characterise higher-education systems through the perspective of university models and missions, noticing relevant aspects regarding the evolution of this institution over time, as well as the transformations undergone. We also consider the main challenges that current higher education systems face in the 21st century. As methodological approaches, we carry out a literature review complemented by a comparative analysis based on data from the higher education systems of ten European countries. The findings show that HEIs can contribute to development through their missions, which are related to the models of higher education. Their first mission (teaching) contributes to improving human capital and attracting highly qualified people to their regions; the second mission (research) improves scientific knowledge which can foster innovative activities; and the third mission (community service) acts as a link between research and business, including patents, business incubators, and collaboration agreements. We also conclude that the challenges of higher education in the 21st century can be categorised essentially in three main areas: (1) globalisation and massification of higher education, as well as the internationalisation of HEIs' missions and diversification of the educational supply to attract new students; (2) new technologies related to the digitalisation of teaching and distance learning; and (3) higher education entrepreneurship, showing the importance of university-company relationships. This paper provides a global setting for a reflection on the role of HEIs in the 21st century, given their connection with society and the need for a more effective contribution to socio-economic development.