The growing consensus that language is distributed into large-scale cortical and subcortical networks has brought with it an increasing focus on the connectional anatomy of language, or how particular fibre pathways connect regions within the language network. Understanding connectivity of the language network could provide critical insights into function, but recent investigations using a variety of methodologies in both humans and non-human primates have provided conflicting accounts of pathways central to language. Some of the pathways classically considered language pathways, such as the arcuate fasciculus, are now argued to be domain-general rather than specialized, which represents a radical shift in perspective. Other pathways described in the non-human primate remain to be verified in humans. In this review, we examine the consensus and controversy in the study of fibre pathway connectivity for language. We focus on seven fibre pathways--the superior longitudinal fasciculus and arcuate fasciculus, the uncinate fasciculus, extreme capsule, middle longitudinal fasciculus, inferior longitudinal fasciculus and inferior fronto-occipital fasciculus--that have been proposed to support language in the human. We examine the methods in humans and non-human primate used to investigate the connectivity of these pathways, the historical context leading to the most current understanding of their anatomy, and the functional and clinical correlates of each pathway with reference to language. We conclude with a challenge for researchers and clinicians to establish a coherent framework within which fibre pathway connectivity can be systematically incorporated to the study of language.