GRANDMA is a world-wide collaboration with the primary scientific goal of studying gravitational-wave sources, discovering their electromagnetic counterparts and characterizing their emission. GRANDMA involves astronomers, astrophysicists, gravitational-wave physicists, and theorists. GRANDMA is now a truly global network of telescopes, with (so far) 30 telescopes in both hemispheres. It incorporates a citizen science programme (Kilonova-Catcher) which constitutes an opportunity to spread the interest in time-domain astronomy. The telescope network is an heterogeneous set of already-existing observing facilities that operate coordinated as a single observatory. Within the network there are wide-field imagers that can observe large areas of the sky to search for optical counterparts, narrow-field instruments that do targeted searches within a predefined list of host-galaxy candidates, and larger telescopes that are devoted to characterization and follow-up of the identified counterparts. Here we present an overview of GRANDMA after the third observing run of the LIGO/VIRGO gravitational-wave observatories in 2019 - 2020 and its ongoing preparation for the forthcoming fourth observational campaign (O4). Additionally, we review the potential of GRANDMA for the discovery and follow-up of other types of astronomical transients.