Background: The detection and description of language impairments in neurodegenerative diseases like Alzheimer's Disease (AD) play an important role in research, clinical diagnosis and intervention. Various methodological protocols have been implemented for the assessment of morphosyntactic abilities in AD; narrative discourse elicitation tasks and structured experimental tasks for production, offline and online structured experimental tasks for comprehension. Very few studies implement and compare different methodological protocols; thus, little is known about the advantages and disadvantages of each methodology. Aims: To discuss and compare the main behavioral methodological approaches and tasks that have been used in psycholinguistic research to assess different aspects of morphosyntactic production and comprehension in individuals with AD at the word and sentence levels. Methods: A narrative review was conducted through searches in the scientific databases Google Scholar, Scopus, Science Direct, MITCogNet, PubMed. Only studies written in English, that reported quantitative data and were published in peer-reviewed journals were considered with respect to their methodological protocol. Moreover, we considered studies that reported research on all stages of the disease and we included only studies that also reported results of a healthy control group. Studies that implemented standardized assessment tools were not considered in this review. Outcomes & Results: The main narrative discourse elicitation tasks implemented for the assessment of morphosyntactic production include interviews, picture-description and story narration, whereas the main structured experimental tasks include sentence completion, constrained sentence production, sentence repetition and naming. Morphosyntactic comprehension in AD has been assessed with the use of structured experimental tasks, both offline (sentence-picture matching, grammaticality judgment) and online (cross-modal naming, speeded sentence acceptability judgment, auditory moving window, word detection, reading). For each task we considered studies that reported results from different morphosyntactic structures and phenomena in as many different languages as possible. Conclusions & Implications: Our review revealed strengths and weaknesses of these methods but also directions for future research. Narrative discourse elicitation tasks as well as structured experimental tasks have been used in a variety of languages, and have uncovered preserved morphosyntactic production but also deficits in people with AD. A combination of narrative discourse elicitation and structured production tasks for the assessment of the same morphosyntactic structure has been rarely used. Regarding comprehension, offline tasks have been implemented in various languages, whereas online tasks have been mainly used in English. Offline and online experimental paradigms have often produced contradictory results even within the same study. The discrepancy between the two paradigms has been attributed to the different working memory demands they impose to the comprehender or to the different parsing processes they tap. Strengths and shortcomings of each methodology are summarized in the paper, and comparisons between different tasks are attempted when this is possible. Thus, the paper may serve as a methodological guide for the study of morphosyntax in AD and possibly in other neurodegenerative diseases.