Vortex coronagraphs are among the most promising solutions to perform high contrast imaging at small angular separations from bright stars. They feature a very small inner working angle (down to the diffraction limit of the telescope), 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 sub-wavelength 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 6 x 10-5 at 2λ=D. Three of them have now been installed on world-leading diffraction-limited infrared cameras, namely 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 imager and on future extremely large telescopes (ELTs). In particular, we will briefly describe our current efforts to improve the manufacturing of mid-infrared AGPMs, to push their operation to shorter wavelengths, and to provide deeper starlight extinction by creating new designs for higher topological charge vortices. Within the VORTEX project, we also plan to develop new image processing techniques tailored to coronagraphic images, and to study some pre- and post-coronagraphic concepts adapted to the vortex coronagraph in order to reduce scattered starlight in the final images.