For image registration, feature detection and description are critical steps that identify the keypoints and describe them for the subsequent matching to estimate the geometric transformation parameters between two images. Recently, there has been a large increase in the research methods of detection operators and description operators, from traditional methods to deep learning methods. To solve the problem, that is, which operator is suitable for specific application problems under different imaging conditions, the paper systematically reviewed commonly used descriptors and detectors from artificial methods to deep learning methods, and the corresponding principle, analysis, and comparative experiments are given as well. We introduce the handcrafted detectors including FAST, BRISK, ORB, SURF, SIFT, and KAZE and the handcrafted descriptors including BRISK, FREAK, BRIEF, SURF, ORB, SIFT, KAZE. At the same time, we review detectors based on deep learning technology including DetNet, TILDE, LIFT, multiscale detector, SuperPoint, and descriptors based on deep learning including pretrained descriptor, Siamese descriptor, LIFT, triplet network, and SuperPoint. Two group of comparison experiments are compared comprehensively and objectively on representative datasets. Finally, we concluded with insightful discussions and conclusions of descriptor and detector selection for specific application problem and hope this survey can be a reference for researchers and engineers in image registration and related fields.