The smart grid is an upgraded concept of electricity network with tight coupling among information, control, and bidirectional communication technologies. Along with the silent features of the ongoing smart grid, cyber-physical security appears to be a deep concern due to its significant dependence on sensing technologies, complex networks of computers, intelligence, and wide-area communication infrastructures. Moreover, the smart grid is an extensive critical infrastructure and vulnerable to coordinated cyber-physical attacks. As a result, cyber-physical attacks cause significant threats to the confidentiality and integrity of the power data, including power outages, cascading failures, and unnecessary expenditure. In this study, security issues of smart grid, including cyber-physical interdependency, attack varieties, detection methods, requirements, standards, challenges, and future prospects, are taken into consideration for both cyber and physical systems, aiming to provide an extensive understanding of vulnerabilities and solutions for the smart power grid. By revealing the inherent features of cyber-physical security in the smart grid, this survey study is addressed to facilitate future research in these two areas.