Efficient and accurate health state estimation is crucial for lithium-ion battery (LIB) performance monitoring and economic evaluation. Effectively estimating the health state of LIBs online is the key but is also the most difficult task for energy storage systems. With high adaptability and applicability advantages, battery health state estimation based on data-driven techniques has attracted extensive attention from researchers around the world. Artificial neural network (ANN)-based methods are often used for state estimations of LIBs. As one of the ANN methods, the Elman neural network (ENN) model has been improved to estimate the battery state more efficiently and accurately. In this paper, an improved ENN estimation method based on electrochemical impedance spectroscopy (EIS) and cuckoo search (CS) is established as the EIS-CS-ENN model to estimate the health state of LIBs. Also, the paper conducts a critical review of various ANN models against the EIS-CS-ENN model. This demonstrates that the EIS-CS-ENN model outperforms other models. The review also proves that, under the same conditions, selecting appropriate health indicators (HIs) according to the mathematical modeling ability and state requirements are the keys in estimating the health state efficiently. In the calculation process, several evaluation indicators are adopted to analyze and compare the modeling accuracy with other existing methods. Through the analysis of the evaluation results and the selection of HIs, conclusions and suggestions are put forward. Also, the robustness of the EIS-CS-ENN model for the health state estimation of LIBs is verified.