Jupiter has the most complex and energetic radiation belts in our Solar System and one of the most challenging space environments to measure and characterize in-depth. Their hazardous environment is also a reason why so many spacecraft avoid flying directly through their most intense regions, thus explaining how Jupiter’s radiation belts have kept many of their secrets so well hidden, despite having been studied for decades. In this paper we argue why these secrets are worth unveiling. Jupiter’s radiation belts and the vast magnetosphere that encloses them constitute an unprecedented physical laboratory, suitable for interdisciplinary and novel scientific investigations: from studying fundamental high energy plasma physics processes which operate throughout the Universe, such as adiabatic charged particle acceleration and nonlinear wave-particle interactions, to exploiting the astrobiological consequences of energetic particle radiation. The in-situ exploration of the uninviting environment of Jupiter’s radiation belts presents us with many challenges in mission design, science planning, instrumentation, and technology. We address these challenges by reviewing the different options that exist for direct and indirect observations of this unique system. We stress the need for new instruments, the value of synergistic Earth and Jupiter-based remote sensing and in-situ investigations, and the vital importance of multi-spacecraft in-situ measurements. While simultaneous, multi-point in-situ observations have long become the standard for exploring electromagnetic interactions in the inner Solar System, they have never taken place at Jupiter or any strongly magnetized planet besides Earth. We conclude that a dedicated multi-spacecraft mission to Jupiter is an essential and obvious way forward for exploring the planet’s radiation belts. Besides guaranteeing numerous discoveries and huge leaps in our understanding of radiation belt systems, such a mission would also enable us to view Jupiter, its extended magnetosphere, moons, and rings under new light, with great benefits for space, planetary, and astrophysical sciences. For all these reasons, in-situ investigations of Jupiter’s radiation belts deserve to be given a high priority in the future exploration of our Solar System. This article is based on a White Paper submitted in response to the European Space Agency’s call for science themes for its Voyage 2050 programme.