The paper provides an overview of Graph Signal Processing (GSP), a field that extends classical signal processing concepts to data defined on irregular graph domains. It begins by introducing core ideas in GSP and their connection to conventional digital signal processing, highlighting the historical development of GSP. The paper then reviews recent advances in basic GSP tools, including sampling, filtering, and graph learning. It also discusses applications of GSP in various fields such as sensor network data processing, biological data analysis, image processing, and machine learning. The authors explore the challenges and future directions in GSP, emphasizing the importance of defining appropriate frequency representations and developing efficient filtering techniques. The paper concludes by outlining the key contributions and open questions in the field.The paper provides an overview of Graph Signal Processing (GSP), a field that extends classical signal processing concepts to data defined on irregular graph domains. It begins by introducing core ideas in GSP and their connection to conventional digital signal processing, highlighting the historical development of GSP. The paper then reviews recent advances in basic GSP tools, including sampling, filtering, and graph learning. It also discusses applications of GSP in various fields such as sensor network data processing, biological data analysis, image processing, and machine learning. The authors explore the challenges and future directions in GSP, emphasizing the importance of defining appropriate frequency representations and developing efficient filtering techniques. The paper concludes by outlining the key contributions and open questions in the field.