Functional neuroimaging revolutionized the study of human language in the late 20th Century, allowing researchers to investigate its underlying cognitive processes in the intact brain. Here, we review how functional MRI (fMRI) in particular has contributed to our understanding of speech comprehension, with a focus on studies of intelligibility. We highlight the use of carefully controlled acoustic stimuli to reveal the underlying hierarchical organization of speech processing systems and cortical (a)symmetries, and discuss the contributions of novel design and analysis techniques to the contextualization of perisylvian regions within wider speech processing networks. Within this, we outline the methodological challenges of fMRI as a technique for investigating speech and describe the innovations that have overcome or mitigated these difficulties. Focussing on multivariate approaches to fMRI, we highlight how these techniques have allowed both local neural representations and broader scale brain systems to be described.