Background: Language is a valuable source of clinical information in Alzheimer’s disease, as it declines concurrently with neurodegeneration. Consequently, speech and language data have been extensively studied in connection with its diagnosis. Objective: Firstly, to summarize the existing findings on the use of artificial intelligence, speech, and language processing to predict cognitive decline in the context of Alzheimer’s disease. Secondly, to detail current research procedures, highlight their limitations, and suggest strategies to address them. Methods: Systematic review of original research between 2000 and 2019, registered in PROSPERO (reference CRD42018116606). An interdisciplinary search covered six databases on engineering (ACM and IEEE), psychology (PsycINFO), medicine (PubMed and Embase), and Web of Science. Bibliographies of relevant papers were screened until December 2019. Results: From 3,654 search results, 51 articles were selected against the eligibility criteria. Four tables summarize their findings: study details (aim, population, interventions, comparisons, methods, and outcomes), data details (size, type, modalities, annotation, balance, availability, and language of study), methodology (pre-processing, feature generation, machine learning, evaluation, and results), and clinical applicability (research implications, clinical potential, risk of bias, and strengths/limitations). Conclusion: Promising results are reported across nearly all 51 studies, but very few have been implemented in clinical research or practice. The main limitations of the field are poor standardization, limited comparability of results, and a degree of disconnect between study aims and clinical applications. Active attempts to close these gaps will support translation of future research into clinical practice.