In the last years, the adoption of Artificial Neural Networks (ANNs) in safety-critical applications has required an in-depth study of their reliability. For this reason, the research community has shown a growing interest in understanding the robustness of artificial computing models to hardware faults. Indeed, several recent studies have demonstrated that hardware faults induced by an external perturbation or due to silicon wear out and aging effects can significantly impact the ANN inference leading to wrong predictions. This work classifies and analyses the principal reliability assessment methodologies based on Fault Injection at different abstraction levels and with different procedures. Some of the most representative academic and industrial works proposed in the literature are described and the principal advantages, and drawbacks are highlighted.