International mobility of higher education institutions' members within the European Union is explicitly encouraged and used as one of the higher education institutions' quality criteria. This paper aims to contribute to the analysis of the phenomenon of international mobility between higher education institutions, especially within the European area in the broad sense, and for which the ERASMUS+ Programme is paradigmatic. The authors have been linked to mobility processes by addressing issues of internationalisation and receiving and sending students and teachers in and out of their institution, and/or hosting them in curricular units taught by them or in other training actions. It is in this context that theoretical reflection has been carried out, to respond to the objective of analysing the relevance of mobility in the internationalisation of higher education institutions and to reflect on questions of its evaluation. It is concluded that there is interest in allowing a mutually enriching scientific dialogue for the personal and professional development of those involved -- students, academics and other staff members. Furthermore, it is institutionally considered that the higher education institution is promoting its quality and image if it provides an in-depth exchange of ideas and practices that foster improvements in teaching and research of the institutions involved. It is also concluded that there is a need for structures to respond to this new reality and that the evaluation processes can contribute to measuring and promoting it.