Alzheimer's disease (AD) is a sort of brain condition that leads to the loss of daily functioning. Early diagnosis and classification of Alzheimer's disease remain unexplored due to the rapid progression of Alzheimer's patients and the absence of effective diagnostic instruments. The accurate and efficient identification of Alzheimer's disease is one of the many objectives of researchers seeking to halt or reverse the illness's progression. The primary purpose of this review is to present a comprehensive analysis and evaluation of the most recent research for AD early recognition and classification using the most advanced deep learning technique. The article presents a simplified explanation of system phases including imaging, preprocessing, learning, and classification. It discusses structural, functional, and molecular imaging in Alzheimer's disease. Magnetic resonance imaging (structural and functional) and positron emission tomography are considered modalities. It examines the pre-processing strategies used to improve quality. In addition, the most prevalent deep learning approaches employed in classification will be reviewed. In addition, it will examine various hurdles in the classification and preprocessing of images, as introduced in a few articles, as well as the approaches used to tackle these issues.