Characterizing heterogeneity of treatment effects (HTE) is a fundamental goal of pharmacoepidemiology, addressing why medications work differently across patient populations. This paper reviews state-of-the-art methods for studying HTE using real-world data (RWD), which offer larger study sizes and more diverse patient populations compared to randomized clinical trials. The paper first defines HTE and discusses its measurement. It then examines three leading approaches to studying HTE: subgroup analysis, disease risk score (DRS) methods, and effect modeling methods. Subgroup analyses offer simplicity, transparency, and provide insights into drug mechanisms. However, they face difficulties in resolving which subgroup or combination of characteristics should be the basis for clinical decision making when multiple effect modifiers are present. DRS methods address some of these limitations by incorporating multiple patient characteristics into a summary score of outcome risk but may obscure insights into mechanisms. Effect modeling methods directly predict individual treatment effects, offering potential for precise HTE characterization, but are prone to model misspecification and may not provide mechanistic insights. The methods each have tradeoffs. Subgroup analysis is straightforward but can lead to spurious associations and does not account for multiple characteristics at once. DRS methods are relatively simple to implement and clinically useful, but may not completely describe HTE or provide mechanistic insight. Effect modeling approaches have great potential for characterizing HTE but are still being developed. Understanding HTE is essential for personalizing treatment strategies to improve patient outcomes. Researchers must weigh the strengths and limitations of each approach when using RWD to study HTE.