Abstract: A cross-lagged structure usually consists of two kinds of effects, autoregressive effects of the prior level of a variable on the current level of itself and cross-lagged effects of the prior level of one variable on the current level of another variable. Longitudinal models with the cross-lagged structure are well recognized as powerful techniques for revealing longitudinal relations between two variables and laying the foundation of diachronic causation. There exist several cross-lagged longitudinal models, while practitioners know little about the association and difference among them, which makes it difficult to choose the most proper one. Although these models are similar in structure, they may differ in the results of estimation. Thus, it is necessary to get a whole picture of these longitudinal models and learn how to compare and choose among them. The present study aims to analyze different cross-lagged longitudinal models and compare them, so as to reveal the importance of model comparison and model selection and provide strategies to select among models. First, we introduce four popular longitudinal models with cross-lagged structure: Cross-Lagged Panel Model (CLPM), Random-Intercept Cross-Lagged Panel Model (RI-CLPM), Latent Curve Model with Structured Residuals (LCM-SR), and Latent Change Score Model (LCS). Then, we clarify the similarities and associations among them. Next, we discuss their differences in various aspects. Finally, we conduct an empirical study to illustrate the procedure of model selection. Results show that: (1) these models are very similar in the model configuration because they all analyze diachronic relations by the cross-lagged structure; (2) CLPM can transform into RI-CLPM, LCM-SR and LCS under certain conditions; (3) different models focus on different developmental characteristics and each of them can provide valuable information on the change process; (4) these models could give different estimation results when applied to the same data set, which may induce different conclusions. We summarize several reference points for selecting a proper longitudinal model in practice: (1) research purpose. If researchers are interested in characterizing the development trajectories, then LCM or LCM-SR is preferred; (2) theoretical knowledge and empirical experience. If there is sufficient evidence showing that the within-person process should be separated from between-person difference, then LCM-SR and RI-CLPM could be considered; (3) the model fitting. Several model fit indices can be used. In summary, longitudinal models with cross-lagged structure play an important role in revealing longitudinal relations between psychological constructs. These models are similar in configuration but vary in modeling basis, premises and data requirements, which may give rise to distinct estimation results and conclusions. Researchers should understand the association and differences among them with considerable insight into model comparison and model selection. It is advisable to try different reasonable models and choose the most proper one for the exploration of longitudinal relations.