Data-dependent hashing methods aim to learn hash functions from the pairwise or triplet relationships among the data, which often lead to low efficiency and low collision rate by only capturing the local distribution of the data. To solve the limitation, we propose central similarity, in which the hash codes of similar data pairs are encouraged to approach a common center and those of dissimilar pairs to converge to different centers. As a new global similarity metric, central similarity can improve the efficiency and retrieval accuracy of hash learning. By introducing a new concept, hash centers, we principally formulate the computation of the proposed central similarity metric, in which the hash centers refer to a set of points scattered in the Hamming space with a sufficient mutual distance between each other. To construct well-separated hash centers, we provide two efficient methods: 1) leveraging the Hadamard matrix and Bernoulli distributions to generate data-independent hash centers and 2) learning data-dependent hash centers from data representations. Based on the proposed similarity metric and hash centers, we propose central similarity quantization (CSQ) that optimizes the central similarity between data points with respect to their hash centers instead of optimizing the local similarity to generate a high-quality deep hash function. We also further improve the CSQ with data-dependent hash centers, dubbed as CSQ with learnable center (CSQ [Formula: see text] ). The proposed CSQ and CSQ [Formula: see text] are generic and applicable to image and video hashing scenarios. We conduct extensive experiments on large-scale image and video retrieval tasks, and the proposed CSQ yields noticeably boosted retrieval performance, i.e., 3%-20% in mean average precision (mAP) over the previous state-of-the-art methods, which also demonstrates that our methods can generate cohesive hash codes for similar data pairs and dispersed hash codes for dissimilar pairs.