Edge computing is a promising paradigm that enhances the capabilities of cloud computing. In order to continue patronizing the computing services, it is essential to conserve a good atmosphere free from all kinds of security and privacy breaches. The security and privacy issues associated with the edge computing environment have narrowed the overall acceptance of the technology as a reliable paradigm. Many researchers have reviewed security and privacy issues in edge computing, but not all have fully investigated the security and privacy requirements. Security and privacy requirements are the objectives that indicate the capabilities as well as functions a system performs in eliminating certain security and privacy vulnerabilities. The paper aims to substantially review the security and privacy requirements of the edge computing and the various technological methods employed by the techniques used in curbing the threats, with the aim of helping future researchers in identifying research opportunities. This paper investigate the current studies and highlights the following: (1) the classification of security and privacy requirements in edge computing, (2) the state of the art techniques deployed in curbing the security and privacy threats, (3) the trends of technological methods employed by the techniques, (4) the metrics used for evaluating the performance of the techniques, (5) the taxonomy of attacks affecting the edge network, and the corresponding technological trend employed in mitigating the attacks, and, (6) research opportunities for future researchers in the area of edge computing security and privacy.