An all-optical Diffractive Deep Neural Network (D2NN) architecture learns to implement various functions or tasks after deep learning-based design of the passive diffractive or reflective substrate layers that work collectively to perform the desired function or task. This architecture was successfully confirmed experimentally by creating 3D-printed D2NNs that learned to implement handwritten classifications and lens function at the terahertz spectrum. This all-optical deep learning framework can perform, at the speed of light, various complex functions and tasks that computer-based neural networks can implement, and will find applications in all-optical image analysis, feature detection and object classification, also enabling new camera designs and optical components that can learn to perform unique tasks using D2NNs. In alternative embodiments, the all-optical D2NN is used as a front-end in conjunction with a trained, digital neural network back-end.