The last two decades have seen a significant amount of interest in bilingual language learning and processing. A number of computational models have also been developed to account for bilingualism, with varying degrees of success. In this article, we first briefly introduce the significance of computational approaches to bilingual language learning, along with a discussion of the major contributions of current models, their implications, and their limitations. We show that the current models have contributed to progress in understanding the bilingual mind, but significant gaps exist. We advocate a new research agenda integrating progress across different disciplines, such as computational neuroscience, natural language processing, and first language acquisition, to construct a pluralist computational account that combines high-level cognitive theories and neurobiological foundations for bilingual language learning. We outline the contributions and promises of this interdisciplinary approach in which we view bilingual language learning as a dynamic, interactive, and developmental process.