Smart grids (SG) draw the attention of cyber attackers due to their vulnerabilities, which are caused by the usage of heterogeneous communication technologies and their distributed nature. While preventing or detecting cyber attacks is a well-studied field of research, making SG more resilient against such threats is a challenging task. This paper provides a classification of the proposed cyber resilience methods against cyber attacks for SG. This classification includes a set of studies that propose cyber-resilient approaches to protect SG and related cyber-physical systems against unforeseen anomalies or deliberate attacks. Each study is briefly analyzed and is associated with the proper cyber resilience technique which is given by the National Institute of Standards and Technology in the Special Publication 800-160. These techniques are also linked to the different states of the typical resilience curve. Consequently, this paper highlights the most critical challenges for achieving cyber resilience, reveals significant cyber resilience aspects that have not been sufficiently considered yet and, finally, proposes scientific areas that should be further researched in order to enhance the cyber resilience of SG.