Handwritten signature is one of the most common methods of biometric authentication, where static and dynamic signature characteristics are used to confirm the user's identity. The existing developments are based on various technologies, such as the neural network, the hidden Markov model, and machine learning algorithms. This topic is rapidly developing, new approaches and algorithms for solving the problem improve the accuracy of verification and learning speed. The purpose of this study is to analyze existing approaches to the signature verification. The most promising algorithm will be used as the basis for the developed authentication system based on a handwritten signature.