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Alzheimer's disease (AD) is the most generally known neurodegenerative disorder, leading to a steady deterioration in cognitive ability. Deep learning models have shown outstanding performance in the diagnosis of AD, and these models do not need any handcrafted feature extraction over conventional machine learning algorithms. Since the 2012 AlexNet accomplishment, the convolutional neural network (CNN) has been progressively utilized by the medical community to assist practitioners to early diagnose AD. This paper explores the current cutting edge applications of CNN on single and multimodality (combination of two or more modalities) neuroimaging data for the classification of AD. An exhaustive systematic search is conducted on four notable databases: Google Scholar, IEEE Xplore, ACM Digital Library, and PubMed in June 2021. The objective of this study is to examine the effectiveness of classification approaches on AD to analyze different kinds of datasets, neuroimaging modalities, preprocessing techniques, and data handling methods. However, CNN has achieved great success in the classification of AD; still, there are a lot of challenges particularly due to scarcity of medical imaging data and its possible scope in this field. [ABSTRACT FROM AUTHOR]