Smart Grid cyber attacks have become more frequent, broader, and intense, attracting more attention. A key component of smart grid cyber security is integrity, which refers to being able to protect information from unauthorized manipulation. These attacks in smart grid are referred to as Load Redistribution (LR) attacks, which are a specific type of False Data Injection Attacks (FDIA). It is a more realistic attack that compromises the data integrity of the measurements. Since the first research on LR attacks was published in 2011, research into LR-based cyber-attacks has grown significantly. As part of the development of coordinated and concerted studies in this field, this paper provides a comprehensive presentation of LR attack taxonomies. The various attributes of the LR attack have also been mapped against the existing literature. Finally, some open issues and research directions are outlined to guide future research and influence further exploration of this ever-expanding area.