This article provides responses to the following questions: what are the major properties of 'remote presence'? What is meant by social presence in e-learning? What are the specific characteristics of the theoretical model of social presence in e-learning (MSP-elearning)? The responses offered are the result of work on characterisation of 'remote presence', conceptualisation and modeling of social presence in e-learning, carried out between 2012 and 2019. Since then, this work has been the subject of several publications, but exclusively in French. This article contributes to give it greater international visibility. Specifically, it outlines the essential aspects of the theoretical model of social presence in e-learning (MSP-elearning), while highlighting its fundamental differences from two other equally interesting theoretical models. This article also contributes to emphasizing that "doing and being together to learn with and from others", despite the geographical distance, is both the subject and the major challenge that this model addresses to the scientific community and practitioners in the field of e-learning.