We present an updated set of near-Earth asteroids with a Yarkovsky-related semimajor axis drift detected from the orbital fit to the astrometry. We find 87 reliable detections after filtering for the signal-to-noise ratio of the Yarkovsky drift estimate and making sure the estimate is compatible with the physical properties of the analysed object. Furthermore, we find a list of 24 marginally significant detections for which future astrometry could result in a Yarkovsky detection. A further outcome of the filtering procedure is a list of detections that we consider spurious because they are either unrealistic or not explicable by the Yarkovsky effect. Among the smallest asteroids of our sample, we determined four detections of solar radiation pressure in addition to the Yarkovsky effect. As the data volume increases in the near future, our goal is to develop methods to generate very long lists of asteroids that have a Yarkovsky effect that is reliably detected and have limited amounts of case by case specific adjustments. Furthermore, we discuss the improvements this work could bring to impact monitoring. In particular, we exhibit two asteroids for which the adoption of a non-gravitational model is needed to make reliable impact predictions.