Meta-analytic techniques have been widely used to synthesize data from animal models of human diseases and conditions, but these analyses often face two statistical challenges due to complex nature of animal data (e.g., multiple effect sizes and multiple species): statistical dependency and confounding heterogeneity. These challenges can lead to unreliable and less informative evidence, which hinders the translation of findings from animal to human studies. In this article, Yefeng Yang and colleagues present a meta-analysis about animal models, showing that these issues are not adequately addressed in current practice. To address these challenges, the authors propose a meta-analytic framework based on multilevel (linear mixed-effects) models. Through conceptualization, formulations, and worked examples, the authors illustrate how this framework can appropriately address these issues while allowing for testing new questions. Additionally, they introduce other advanced techniques such as multivariate models, robust variance estimation, and meta-analysis of emergent effect sizes, which can deliver robust inferences and novel biological insights. The authors also provide a tutorial with annotated R code to demonstrate the implementation of these techniques.