Alzheimer’s disease (AD) is a brain-related disease in which the condition of the patient gets worse with time. AD is not a curable disease by any medication. It is impossible to halt the death of brain cells, but with the help of medication, the effects of AD can be delayed. As not all MCI patients will suffer from AD, it is required to accurately diagnose whether a mild cognitive impaired (MCI) patient will convert to AD (namely MCI converter MCI-C) or not (namely MCI non-converter MCI-NC), during early diagnosis. There are two modalities, positron emission tomography (PET) and magnetic resonance image (MRI), used by a physician for the diagnosis of Alzheimer’s disease. Machine learning and deep learning perform exceptionally well in the field of computer vision where there is a requirement to extract information from high-dimensional data. Researchers use deep learning models in the field of medicine for diagnosis, prognosis, and even to predict the future health of the patient under medication. This study is a systematic review of publications using machine learning and deep learning methods for early classification of normal cognitive (NC) and Alzheimer’s disease (AD).This study is an effort to provide the details of the two most commonly used modalities PET and MRI for the identification of AD, and to evaluate the performance of both modalities while working with different classifiers.