ELI Beamlines is a newly constructed petawatt (PW) laser-based accelerator facility. Its flagship laser has a nominal peak power of 10 PW with a pulse duration of 150 fs. The radiation fields emerging from the laser-target interactions will be pulsed and made of mixed particles of high intensity and energy, thus posing new and daunting challenges compared to conventional radiation protection. The civil engineering constraints of a laser facility bring localized weaknesses to the shielding structures. The ultrashort pulses in conjunction with ultrahigh dose rates strain the capabilities of the commercially available radiation detectors. The complexity of modeling laser-target interactions and the resulting ionizing radiation complicates the radiation protection calculations. This paper is a review of the radiation protection challenges at ELI Beamlines, the adopted solutions, and the practices to minimize the harmful effects of ionizing radiation linked to its activities. Some of the presented solutions may have universal validity, while others are specific to this site and can only serve as an inspiration.