(abridged) Vortex coronagraphs are among the most promising solutions to perform high contrast imaging at small angular separations. They feature a very small inner working angle, a clear 360 degree discovery space, have demonstrated very high contrast capabilities, are easy to implement on high-contrast imaging instruments, and have already been extensively tested on the sky. Since 2005, we have been designing, developing and testing an implementation of the charge-2 vector vortex phase mask based on concentric subwavelength gratings, referred to as the Annular Groove Phase Mask (AGPM). Science-grade mid-infrared AGPMs were produced in 2012 for the first time, using plasma etching on synthetic diamond substrates. They have been validated on a coronagraphic test bench, showing broadband peak rejection up to 500:1 in the L band, which translates into a raw contrast of about $6times 10^{-5}$ at $2 lambda/D$. Three of them have now been installed on world-leading diffraction-limited infrared cameras (VLT/NACO, VLT/VISIR and LBT/LMIRCam). During the science verification observations with our L-band AGPM on NACO, we observed the beta Pictoris system and obtained unprecedented sensitivity limits to planetary companions down to the diffraction limit ($0.1$). More recently, we obtained new images of the HR 8799 system at L band during the AGPM first light on LMIRCam. After reviewing these first results obtained with mid-infrared AGPMs, we will discuss the short- and mid-term goals of the on-going VORTEX project, which aims to improve the performance of our vortex phase masks for future applications on second-generation high-contrast imagers and on future extremely large telescopes (ELTs).