  Graph signal processing (GSP) generalizes signal processing (SP) tasks to
signals living on non-Euclidean domains whose structure can be captured by a
weighted graph. Graphs are versatile, able to model irregular interactions,
easy to interpret, and endowed with a corpus of mathematical results, rendering
them natural candidates to serve as the basis for a theory of processing
signals in more irregular domains. In this article, we provide an overview of
the evolution of GSP, from its origins to the challenges ahead. The first half
is devoted to reviewing the history of GSP and explaining how it gave rise to
an encompassing framework that shares multiple similarities with SP. A key
message is that GSP has been critical to develop novel and technically sound
tools, theory, and algorithms that, by leveraging analogies with and the
insights of digital SP, provide new ways to analyze, process, and learn from
graph signals. In the second half, we shift focus to review the impact of GSP
on other disciplines. First, we look at the use of GSP in data science
problems, including graph learning and graph-based deep learning. Second, we
discuss the impact of GSP on applications, including neuroscience and image and
video processing. We conclude with a brief discussion of the emerging and
future directions of GSP.
