This Perspective discusses the potential of free-space optical systems based on engineered surfaces for advancing optical computing. Diffractive networks bring deep-learning principles into the design and operation of free-space optical systems to create new functionalities. Meta-surfaces with subwavelength units enable independent control over different properties of light and can significantly improve computational throughput and data-transfer bandwidth. Unlike integrated photonics-based systems, free-space optical processors have direct access to all optical degrees of freedom without preprocessing. To realize their full potential, diffractive surfaces and metasurfaces must co-evolve in design, fabrication, and integration. Free-space optical processors can perform polarization, spatial, and spectral processing of waves. They offer advantages in visual information processing due to direct access to 2D or 3D optical information. Free-space optical computing systems have undergone a paradigm shift due to emerging deep-learning methods and unique fabrication technologies. This Perspective focuses on data-driven design and fabrication of diffractive surfaces and metasurfaces. These systems can perform polarization processing, spatial processing, universal linear transformations, and spectral & temporal processing of waves. The synergy between diffractive surfaces and metasurfaces in free-space optical computing has not been explored in depth. This Perspective highlights emerging opportunities and challenges in free-space optical computing, including computational accuracy, dynamic reconfigurability, speed and scalability of fabrication, and diffraction efficiency. The Perspective also discusses design principles of spatially-structured surfaces for computing, diffractive surfaces, metasurfaces, and their applications in optical computing. It covers the capabilities of free-space optical processors in statistical inference, data classification, universal linear transformations, and optical processing of spatial, spectral, and temporal information. The Perspective also discusses the challenges in free-space optical computing, including diffraction efficiency, power requirements, tunability, reconfigurability, fabrication complexity, computation speed, parallelism, and scalability. The Perspective concludes that free-space optical computing has the potential to revolutionize various technologies, including optical machine learning, statistical inference, computational imaging, and telecommunications.This Perspective discusses the potential of free-space optical systems based on engineered surfaces for advancing optical computing. Diffractive networks bring deep-learning principles into the design and operation of free-space optical systems to create new functionalities. Meta-surfaces with subwavelength units enable independent control over different properties of light and can significantly improve computational throughput and data-transfer bandwidth. Unlike integrated photonics-based systems, free-space optical processors have direct access to all optical degrees of freedom without preprocessing. To realize their full potential, diffractive surfaces and metasurfaces must co-evolve in design, fabrication, and integration. Free-space optical processors can perform polarization, spatial, and spectral processing of waves. They offer advantages in visual information processing due to direct access to 2D or 3D optical information. Free-space optical computing systems have undergone a paradigm shift due to emerging deep-learning methods and unique fabrication technologies. This Perspective focuses on data-driven design and fabrication of diffractive surfaces and metasurfaces. These systems can perform polarization processing, spatial processing, universal linear transformations, and spectral & temporal processing of waves. The synergy between diffractive surfaces and metasurfaces in free-space optical computing has not been explored in depth. This Perspective highlights emerging opportunities and challenges in free-space optical computing, including computational accuracy, dynamic reconfigurability, speed and scalability of fabrication, and diffraction efficiency. The Perspective also discusses design principles of spatially-structured surfaces for computing, diffractive surfaces, metasurfaces, and their applications in optical computing. It covers the capabilities of free-space optical processors in statistical inference, data classification, universal linear transformations, and optical processing of spatial, spectral, and temporal information. The Perspective also discusses the challenges in free-space optical computing, including diffraction efficiency, power requirements, tunability, reconfigurability, fabrication complexity, computation speed, parallelism, and scalability. The Perspective concludes that free-space optical computing has the potential to revolutionize various technologies, including optical machine learning, statistical inference, computational imaging, and telecommunications.