Blockchain has attracted more and more attention of academia, industry, and government in recent decades. Different usage demands have inspired various blockchain designs, forming different blockchain systems, which leads to information islands. Many cross-chain technologies have been proposed to link different blockchains together and expand the utility of blockchain. Nevertheless, the cross-chain technology is still in its infancy, which faces many problems that retard its wide application, for example, the issues related to security, privacy, and effectiveness. In order to further investigate cross-chain technologies, it is essential to understand its current state of arts. Although there are some surveys about cross-chain technologies driven by specific demands, the literature still lacks a comprehensive survey focusing on security, privacy, and effectiveness of cross-chain technologies. In this paper, we provide a review on existing cross-chain technologies based on a comprehensive set of criteria on security, privacy, and other performance. We first propose a blockchain interoperability architecture for the purpose of analyzing potential threats and problems regarding security, privacy, and effectiveness. We then summarize a set of criteria regarding these quality attributes. Next, we comprehensively review the representative works on cross-chain technologies according to a taxonomy based on applied types of techniques and cross-chain purposes. In each work review, we provide a serious discussion on its pros and cons by employing our proposed criteria. Finally, based on our review and analysis, we figure out a number of open issues and step ahead to direct future research directions on cross-chain technologies.