For deep space exploration, radiation effects on astronauts, and on items fundamental for life support systems, must be kept under a pre-agreed threshold to avoid detrimental outcomes. Therefore, it is fundamental to achieve a deep knowledge on the radiation spatial and temporal variability in the different mission scenarios as well as on the responses of different organisms to space-relevant radiation. In this paper, we first consider the radiation issue for space exploration from a physics point of view by giving an overview of the topics related to the spatial and temporal variability of space radiation, as well as on measurement and simulation of irradiation, then we focus on biological issues converging the attention on plants as one of the fundamental components of Bioregenerative Life Support Systems (BLSS). In fact, plants in BLSS act as regenerators of resources (i.e. oxygen production, carbon dioxide removal, water and wastes recycling) and producers of fresh food. In particular, we summarize some basic statements on plant radio-resistance deriving from recent literature and concentrate on endpoints critical for the development of Space agriculture. We finally indicate some perspective, suggesting the direction future research should follow to standardize methods and protocols for irradiation experiments moving towards studies to validate with space-relevant radiation the current knowledge. Indeed, the latter derives instead from experiments conducted with different radiation types and doses and often with not space-oriented scopes.