Adaptive Optics for astronomy has revolutionized the ground-based telescopes by providing the highest achievable image quality of the world. All the current 8/10m telescopes are progressively turned into adaptive telescopes, relying on complex AO systems integrated inside the telescope itself, and providing high-resolution images to the instrumentation downstream. The next step forward will come from the so-called Extremely Large Telescopes (ELTs), with facilities now providing 100% of their science assisted by AO. As a consequence, the astronomical community exposed to AO-corrected data is growing exponentially. However, the exceptional advancement in AO technology and observational capability has not been followed by a comparable advancement in the development of the associated data analysis methods. In particular, a critical point when analyzing AO data concerns the separation of the instrument contribution from the intrinsic signature of the astrophysical signal. This can only be achieved by an accurate estimation of the instrument Point Spread Function (PSF). An AO system increases the energy concentration of the PSF, but this latter suffers from a complex shape combining spatial, spectral and temporal variability. The main challenge for the AO PSF comes from the stochastic effects induced by the environment. The AO system partially compensates the aberrations induced by the atmosphere and the telescope, but the strength and spatial structure of the atmospheric turbulence is constantly evolving on time scales faster than seconds. In this context, deriving an accurate PSF model associated with every AO-observation remains a challenge, and the lack of PSF knowledge often represents the main limitation when analyzing AO data. Gains by factors 2 to 5 in science performance are achievable if accurate (%-level) PSF models would be available. Extracting the AO-PSF from the science images quickly fails for extragalactic fields that are usually empty of reference stars, or dense stellar fields for which crowding prevents the extraction of a single PSF. Moreover, the situation is particularly critical for integral Field Spectrographs (IFS), as their fields of view are generally too small to contain any point source that could act as PSF calibrator. When the PSF information cannot be properly extracted from the science image, an alternative approach is to predict the PSF shape based on auxiliary data. This is precisely the objective of APPLY, to provide the community with operational solutions for AO-PSF prediction, relevant to all conditions and all science cases. This is achieved thanks to (i) recent breakthroughs led by our group on AO-PSF modeling, (ii) taking advantage of innovative data processing methods and (iii) gathering a multidisciplinary team of astronomers, data specialists and AO experts. The major strength of APPLY relies in an integrated approach, where not only the PSF is provided, but the estimated PSFs are coupled with dedicated reduction tools and validated against “PSF science verification” observations. The optimization of the whole data-processing chain is carried-out with data processing specialists, and the quantitative scientific impact and critical feedback on the process is evaluated with astronomers. For that, the project takes advantage of access to large on-sky data-sets, as well as simulated data to demonstrate the pipeline accuracy in a controlled environment. The methodology is developed over three main Work Packages (WPs), dedicated to three major instruments: MUSE @ ESO-VLT, OSIRIS @ KECK and HARMONI @ ELT. But the methodology developed by APPLY is very general, and applications to other instruments will also be explored. By providing the predicted PSF with each single observation, we aim at impacting the largest community possible, and propose a new breakthrough toward the optimization of the scientific returns of AO observations.