In many places throughout the world, children are totally immersed in an L2 reading curriculum with minimal attention to their native language literacy and to their L2 spoken language level. These children are thus confronted with the task of learning to read in a language that they have yet to master. Whatever the context of learning, L2 reading reflects a learned sensitivity to the systematic relationships among the surface representations of words and their meanings, and their unification into sentences and text in the target language. It is assumed that shared brain regions are involved in first language (L1) and second language (L2) reading (convergence hypothesis), although different perceptual, linguistic, and computation demands of the second language may involve additional supporting brain regions during learning. In this presentation, it will be argued that processes of learning to read in a second language can be considered highly intralingual, i.e. to a large extent controlled by L2 processes with only little L1 involvement. On this view, L2 learners rely on similar processes as L1 learners but they are just less efficient in building up visual text representations in the target language. In a set of cross-linguistic neurocognitive studies, it will be shown that L2 processes in learning to read can to a high degree be considered intralingual. In a complementary set of longitudinal studies, it will also be shown how processes in learning to read in L2 may be hampered due to complexities in word learning, word to text integration and reading comprehension.