In this systematic umbrella review we aggregate the current knowledge of how virtual and augmented reality technologies are applicable to and impact remote learning in higher education; specifically, how they impact such learning outcomes as performance and engagement in all stages of higher education from course preparation to student evaluation and grading. This review was done as part of a state wide research effort of Latvia, to mitigate the impact of COVID-19 and specifically to provide a framework for a technological transformation of education in this context. In this work we search the Scopus and Web of Science databases for articles describing the use of virtual and/or augmented reality technologies in remote learning for higher education and their impact on learning outcomes. We identified 68 articles from which, after multiple screening and eligibility phases, nine review articles were left for extraction phase in which 30 structural elements with corresponding interventions and measured effects were extracted. Of these, 24 interventions had a measured effect on student performance (11 positive, seven negative, six no impact) and six interventions had a measured effect on student engagement (all six positive).