  Rapidly growing demands for high-performance computing, powerful data
processing systems, and big data necessitate the advent of novel optical
devices to perform demanding computing processes effectively. Due to its
unprecedented growth in the past two decades, the field of meta-optics offers a
viable solution for spatially, spectrally, and/or even temporally sculpting
amplitude, phase, polarization, and/or dispersion of optical wavefronts. In
this Review, we discuss state-of-the-art developments as well as emerging
trends in computational meta-structures as disruptive platforms for spatial
optical analog computation. Two fundamental approaches based on general
concepts of spatial Fourier transformation and Green's function are discussed
in detail. Moreover, numerical investigations and experimental demonstrations
of computational optical surfaces and meta-structures for solving a diverse set
of mathematical problems (e.g., integro-differentiation and convolution
equations) necessary for on-demand applications (e.g., edge detection) are
reviewed. Finally, we explore the current challenges and the potential
resolutions in computational meta-optics followed by our perspective on future
research directions and possible developments in this promising area.
