  Geometric data acquired from real-world scenes, e.g., 2D depth images, 3D
point clouds, and 4D dynamic point clouds, have found a wide range of
applications including immersive telepresence, autonomous driving,
surveillance, etc. Due to irregular sampling patterns of most geometric data,
traditional image/video processing methodologies are limited, while Graph
Signal Processing (GSP) -- a fast-developing field in the signal processing
community -- enables processing signals that reside on irregular domains and
plays a critical role in numerous applications of geometric data from low-level
processing to high-level analysis. To further advance the research in this
field, we provide the first timely and comprehensive overview of GSP
methodologies for geometric data in a unified manner by bridging the
connections between geometric data and graphs, among the various geometric data
modalities, and with spectral/nodal graph filtering techniques. We also discuss
the recently developed Graph Neural Networks (GNNs) and interpret the operation
of these networks from the perspective of GSP. We conclude with a brief
discussion of open problems and challenges.
