Since its first light at the VLT in 2012, the Annular Groove Phase Mask (AGPM) has been used to implement vortex coronagraphy into AO-assisted infrared cameras at two additional world-leading observatories: the Keck Observatory and the LBT. In this paper, we review the status of these endeavors, and briefly highlight the main scientific results obtained so far. We explore the performance of the AGPM vortex coronagraph as a function of instrumental constraints, and identify the main limitations to the sensitivity to faint, off-axis companions in high-contrast imaging. These limitations include the AGPM itself, non-common path aberrations, as well as the data processing pipeline; we briefly describe our on-going efforts to further improve these various aspects. Based on the lessons learned from the first five years of on-sky exploitation of the AGPM, we are now preparing its implementation in a new generation of high-contrast imaging instruments. We detail the specificities of these instruments, and how they will enable the full potential of vortex coronagraphy to be unleashed in the future. In particular, we explain how the AGPM will be used to hunt for planets in the habitable zone of alpha Centauri A and B with a refurbished, AO-assisted version of the VISIR mid-infrared camera at the VLT (aka the NEAR project), and how this project paves the way towards mid-infrared coronagraphy on the ELT with the METIS instrument. We also discuss future LM-band applications of the AGPM with VLT/ERIS, ELT/METIS, and with a proposed upgrade of Keck/NIRC2, as well as future applications at shorter wavelengths, such as a possible upgrade of VLT/SPHERE with a K-band AGPM.