In addition, memristors have the potential to revolutionize artificial intelligence and machine learning by enabling the development of more efficient and powerful neural networks. Moreover, their non-volatile nature allows for instant-on capabilities and low power consumption, making them ideal for energy-efficient devices and Internet of Things (IoT) applications. Additionally, memristors are used for analog design and signal processing applications [13; 14; 15; 16; 17]. They offer the ability to store and manipulate continuous signals, making them suitable for applications such as audio and video processing, signal filtering, signal amplification, radio frequency design, and control systems. It allows for more accurate diagnoses and treatment planning. Furthermore, memristors have the advantage of being highly scalable and compatible with existing semiconductor fabrication processes, allowing for compact and efficient circuit designs. This makes them a promising technology for miniaturized electronic devices and integrated circuits. Also, their non-volatile nature ensures that data can be retained even when power is lost, making them suitable for applications requiring reliable and persistent storage. They are commonly used in various applications, such as telecommunications, mobile networks, medical imaging, healthcare monitoring, sensor data processing, and robotics. In the telecommunications industry and mobile networks, memristors are particularly utilized for storing and processing critical data efficiently and for firmware updates in network infrastructure equipment. Medical imaging and healthcare monitoring systems benefit from the compactness and reliability of these memory devices, which enable faster and more accurate image analysis and can help track vital signs and detect abnormalities in real-time. Additionally, memristors play a crucial role in sensor data processing by enabling quick and reliable data analysis for various applications. Lastly, memristors contribute to advancements in robotics by enhancing the performance and intelligence of robotic systems through efficient data storage and processing capabilities. Various reviews on memristors have been published in the literature. These reviews cover topics such as memristor theory, history, properties, models, and fabrication techniques. Additionally, these reviews have highlighted the potential applications of memristors in the digital domain, including neuromorphic computing, artificial intelligence, logic operations, and memory storage devices. Recently, researchers' efforts have focused on investigating new memristor-based analog design techniques and methodologies. By incorporating memristors into analog circuits, researchers hope to enhance the functionality and energy efficiency of various electronic systems, paving the way for innovative advancements in a wide range of fields. Additionally, these efforts aim to further expand the capabilities and applications of memristors beyond the digital domain. However, further research is needed to fully understand their behavior and optimize their performance for practical analog applications. This review aims to provide a comprehensive overview of the current state of research on memristor-based analog circuits and highlight key challenges and opportunities for future development in this field. Memristors can revolutionize analog circuit design by enabling new functionalities and capabilities like adaptive filtering and reconfigurable circuits. These advancements could lead to significant improvements in communication systems, signal processing, and biomedical devices. The paper also discusses the challenges and prospects of memristor technology, emphasizing its potential for creating more efficient and powerful systems. Overall, the potential of memristors in analog applications is vast and continues to drive innovation in the field of electronics. The rest of the paper is organized as follows: Section 2 presents the principles, models, materials and characteristics of memristors.