Nowadays, the verification of handwritten signatures has become an effective research field in computer vision as well as machine learning. Signature verification is naturally formulated as a machine-learning task. This task is performed by determining if the signature is genuine or forged. Therefore, it is considered a two‐class classification issue. Since handwritten signatures are widely used in legal documents and financial transactions, it is important for researchers to select an efficient machine-learning technique for verifying these signatures and to avoid forgeries that may cause many losses to customers. So far, great outcomes have been obtained when using machine learning techniques in terms of equal error rates and calculations. This paper presents a comprehensive review of the latest studies and results in the last 10 years in the field of online and offline handwritten signature verification. More than 20 research papers were used to make a comparison between datasets, feature extraction, and classification techniques used in each system, taking into consideration the problems that occur in each. In addition, the general limitations and advantages of machine-learning techniques that are used to classify or extract signature features were summarized in the form of a table. We also present the general steps of the verification system and a list of the most considerable datasets available in online and offline fields.