What is the future of grey literature? Is open science an opportunity for grey literature (more grey literature, more visibility and impact of grey literature), just another challenge (issues that need awareness and further action) or even a threat (less grey documents, less impact)? The following paper presents findings from a systematic review of recent studies on grey literature and open science; it includes recent reports and initiatives, and builds on our own former empirical research work. The findings of the review are presented in four sections: the concept of bibliodiversity (production); the development of open repositories (dissemination); the transformation of research assessment (evaluation); the application of FAIR principles (processing). Some leading questions: Which is the common part of the concepts of bibliodiversity (Jussieu Call) and grey literature, and what does this mean for the future of grey literature? Which are the issues of grey literature in open repositories, and how do repositories impact the dissemination of grey literature? How do the recent initiatives for a new system of research assessment affect the grey literature (San Francisco Declaration DORA, European Commission Scoping report, OSEC Call of Paris)? Are the FAIR principles relevant for the processing of grey literature, and if so, which ones and in which way? The paper is a scientific contribution to the analysis of the development of grey literature in the academic research environment of the 21st century. It is a rejoinder of the 2021 panel discussion on the “Next Generation Grey”; it tries to sum up what is known about grey literature and open science, and it makes some recommendations for grey literature producers, service providers and repository managers.