An accelerated electron generates an electromagnetic field, which in turn reacts on the electron itself. This “radiaction reaction” phenomenon has a long history in classical electrodynamics and it is still an open question in the quantum regime. Two experiments used the ASTRA-GEMINI laser to characterize radiation reaction effects in the collision of a superintense, ultrashort pulse with a bunch of high-energy electrons, generated by laser-plasma acceleration. The results suggest a preliminary evidence of quantum effects, but leave the question open. In this Viewpoint we give a critical comment on the experiments and future perspectives.