Graph Signal Processing (GSP) is a field that extends classical signal processing concepts to data defined on irregular graph domains. This paper provides an overview of GSP, its connection to conventional digital signal processing, and recent advances in developing basic GSP tools such as sampling, filtering, and graph learning. It also reviews progress in various application areas, including sensor networks, biological data, and image processing. GSP allows for the extension of classical signal processing concepts like Fourier transforms, filtering, and frequency response to graph-structured data. It also enables tasks such as sampling, denoising, and learning the underlying structure of graph signals. The paper discusses the challenges and open questions in GSP, including the definition of frequency, the choice of shift operators, and the development of efficient filterbanks. It also highlights the importance of spectral graph theory in understanding the properties of graph signals and the role of graph Laplacians in defining frequency representations. The paper concludes with an outline of the rest of the paper, which covers key ingredients of GSP, state-of-the-art topics, and challenges in the field.Graph Signal Processing (GSP) is a field that extends classical signal processing concepts to data defined on irregular graph domains. This paper provides an overview of GSP, its connection to conventional digital signal processing, and recent advances in developing basic GSP tools such as sampling, filtering, and graph learning. It also reviews progress in various application areas, including sensor networks, biological data, and image processing. GSP allows for the extension of classical signal processing concepts like Fourier transforms, filtering, and frequency response to graph-structured data. It also enables tasks such as sampling, denoising, and learning the underlying structure of graph signals. The paper discusses the challenges and open questions in GSP, including the definition of frequency, the choice of shift operators, and the development of efficient filterbanks. It also highlights the importance of spectral graph theory in understanding the properties of graph signals and the role of graph Laplacians in defining frequency representations. The paper concludes with an outline of the rest of the paper, which covers key ingredients of GSP, state-of-the-art topics, and challenges in the field.