Modern electric power grid, known as the Smart Grid, has fast transformed the isolated and centrally controlled power system to a fast and massively connected cyber-physical system that benefits from the revolutions happening in the communications and the fast adoption of Internet of Things devices. While the synergy of a vast number of cyber-physical entities has allowed the Smart Grid to be much more effective and sustainable in meeting the growing global energy challenges, it has also brought with it a large number of vulnerabilities resulting in breaches of data integrity, confidentiality and availability. False data injection (FDI) appears to be among the most critical cyberattacks and has been a focal point interest for both research and industry. To this end, this paper presents a comprehensive review in the recent advances of the defence countermeasures of the FDI attacks in the Smart Grid infrastructure. Relevant existing literature are evaluated and compared in terms of their theoretical and practical significance to the Smart Grid cybersecurity. In conclusion, a range of technical limitations of existing false data attack detection researches are identified, and a number of future research directions are recommended.