The use of radiomics and artificial intelligence applied for the diagnosis and monitoring of Alzheimer’s disease has developed in recent years. However, this approach is not yet completely applicable in clinical practice. The aim of this paper is to provide a systematic analysis of the studies that have included the use of radiomics from different imaging techniques and artificial intelligence for the diagnosis and monitoring of Alzheimer’s disease in order to improve the clinical outcomes and quality of life of older patients. A systematic review of the literature was conducted in February 2023, analyzing manuscripts and articles of the last 5 years from the PubMed, Scopus and Embase databases. All studies concerning discrimination among Alzheimer’s disease, Mild Cognitive Impairment and healthy older people performing radiomics analysis through machine and deep learning were included. A total of 15 papers were included. The results showed a very good performance of this approach in the differentiating Alzheimer’s disease patients—both at the dementia and pre-dementia phases of the disease—from healthy older people. In summary, radiomics and AI can be valuable tools for diagnosing and monitoring the progression of Alzheimer’s disease, potentially leading to earlier and more accurate diagnosis and treatment. However, the results reported by this review should be read with great caution, keeping in mind that imaging alone is not enough to identify dementia due to Alzheimer’s.