Two-dimensional (2D) materials have many unique properties, which can be exploited in various applications. In particular, electronic devices based on 2D materials should ideally be suited for the operation in outer cosmic space due to their low weight, small size and low power consumption. This brings about the issue of their radiation hardness, or tolerance, which has recently been addressed in a number of studies. The results of these investigations are somewhat counterintuitive: although one can naively expect that atomically thin structures should easily be destroyed by the beams of energetic particles, the devices made from 2D materials were reported to exhibit extraordinary radiation hardness. In this Focus article, an overview of the recent studies on the subject is given, followed by the discussion of the origin of the reported high tolerance, which is inherently related to the response of 2D materials, the systems with the reduced dimensionality, to irradiation. The analysis of the experimental and theoretical data on the behavior of 2D systems under irradiation indicates that although free-standing 2D materials can indeed be referred to as radiation resilient systems under irradiation conditions corresponding to the outer space, this is generally not the case, as the environment, e.g., the substrate, can strongly influence the radiation tolerance of 2D materials and devices based on these systems.