Background and Objectives: Recently, longitudinal studies of Alzheimer's disease have gathered a substantial amount of neuroimaging data. New methods are needed to successfully leverage and distill meaningful information on the progression of the disease from the deluge of available data. Machine learning has been used successfully for many different tasks, including neuroimaging related problems. In this paper, we review recent statistical and machine learning applications in Alzheimer's disease using longitudinal neuroimaging. Methods: We search for papers using longitudinal imaging data, focused on Alzheimer's Disease and published between 2007 and 2019 on four different search engines. Results: After the search, we obtain 104 relevant papers. We analyze their approach to typical challenges in longitudinal data analysis, such as missing data and variability in the number and extent of acquisitions. Conclusions: Reviewed works show that machine learning methods using longitudinal data have potential for disease progression modelling and computer-aided diagnosis. We compare results and models, and propose future research directions in the field. (C) 2020 Elsevier B.V. All rights reserved.