Cyber-physical attacks are the main substantial threats facing the utilization and development of the various smart grid technologies. Among these attacks, false data injection attack represents a main category with its widely varied types and impacts that have been extensively reported recently. In addressing this threat, several detection algorithms have been developed in the last few years. These were either model-based or data-driven algorithms. This paper provides an intensive summary of these algorithms by categorizing them and elaborating on the pros and cons of each category. The paper starts by introducing the various cyber-physical attacks along with the main reported incidents in history. The significance and the impacts of the false data injection attacks are then reported. The concluding remarks present the main criteria that should be considered in developing future detection algorithms for the false data injection attacks.