Over the last 40 years, neurolinguistics has honed our understanding of language (dys)functions through studies on diverse stimulus types. Yet, most studies have employed (pseudo)randomized sequences of isolated, decontextualized words or sentences, neglecting more naturalistic manifestations of language. Do key findings in such traditional paradigms generalize onto context-rich materials, such as narrative texts? And can specific neural disorders be detected by analyzing spontaneous speech? In this presentation, I will survey recent findings from discourse-level approaches to basic and translational neurolinguistics. Our team has developed a multi-methodological framework for healthy persons and neurological patients, yielding new evidence to address the two questions mentioned above. First, we have shown that the same neural networks engaged by specific single-item categories (e.g., action-related and socially-laden words) are critically recruited when such stimuli are embedded in context-rich, cohesive, and coherent stories. Second, our machine learning studies suggest that fine-grained acoustic (e.g., articulatory) and textual (e.g., semantic) properties of spontaneous verbal production allow identifying persons with different neurodegenerative disorders and predicting symptom severity. These lines of work pave the way for a naturalistic neurolinguistic agenda, expanding recent neurocognitive models and revealing candidate markers of highly prevalent brain diseases.