Power networks are among the most critical infrastructures of any society, since other infrastructures are dependent on power and energy systems. Recently, there has been a trend toward harnessing Information Technology (IT) in power networks to enhance their performance and improve their consumer centricity. This movement, however, has exposed power systems to cyberattacks. Among various types of cyber intrusions, False Data Injection Attack (FDIA) is the most important one, since it stealthily intercepts the legitimate traffic and/or injects malicious data into the system, thus resulting in severe physical and economic damages. There has been a substantial increase in the number of reported FDIAs in recent years, which indicates the necessity of extensive research on vulnerabilities of power systems to FDIAs, probable attack models, impacts of such intrusions, and the possible preventive and detective measures. On this basis, this article presents a comprehensive review of FDIAs in power networks, with a particular focus on attack targets and adversarial methods. Additionally, it elaborates on various types of FDIAs, their implementation steps and strategies, and the vulnerabilities of various components and schemes to this type of attack. Finally, the it briefly discusses FDIA detection techniques in power grids.