Various optical feature extraction and spatial filters for scale, rotation and shift invariant pattern recognition are reviewed. Many methods are based on the circular Fourier and radial Mellin transform (FMT). With the pure imaginary Mellin transform order s=-jω, the FMT may be implemented using a polar-log coordinate transform followed by 2D Fourier transform. With positive integer orders s, the FMT’s yield the moment invariants. Invariant pattern recognition is made using the regular moments for image normalization, the Hu’s moment invariants, the Zemike moment invariants, the complex moments, the Fourier-Mellin descriptors, and the orthogonal Fourier-Mellin moments. The polar coordinate Fourier-Mellin moments use more low order moments and do not suffer from information suppression, information redundancy and are more robust against noise. Optically generated image moments may be combined to the moment invariants. The FMT may also be directly generated in an optical correlator using the Fourier-Mellin spatial filters (FMF’s), that allow an additional shift invariance. An optoneural system using the FMF and a neural network is presented.