Since 2007 the AGILE satellite of the Agenzia Spaziale Italiana (ASI) is observing the Sky with the two imagers SuperAGILE (18 - 60 keV) and the Gamma Ray Imaging Detector (25 MeV - 30 GeV) and the non-imaging Minicalorimeter (500 keV - 100 MeV). Up to now, AGILE obtained four firm detections above 25 MeV (GRB 080514B, GRB 090401B, GRB 090510 and GRB 100724B) and other bursts were detected with lower statistical confidence in the same energy band. We review the status and the results of the observation of GRBs with AGILE and we discuss the the main features (extended and delayed emission, possible spectral evolution) of the observed events. We discuss also the theoretical implications of the not-detected GRBs in the AGILE field of view.