Many scientific questions are to understand and reveal the causal mechanisms from observational study data or experimental data. Over the past several decades, there has been a large number of developments to render causal inferences from observed data. Most developments are designed to estimate the mean difference between treated and control groups that is often called the average treatment effect (ATE), and rely on identifying assumptions to allow causal interpretation. However, more specific treatment effects beyond the ATE can be estimated under the same assumptions. For example, instead of estimating the mean of potential outcomes in a group, we may want to estimate the distribution of the potential outcomes. Understanding the distribution implies understanding the mean, but not vice versa. Therefore, more sophisticated causal inference can be made from the data. The dissertation focuses on causal inference in observational studies, and discusses three main achievements. First, in instrumental variable (IV) models, we propose a novel nonparametric likelihood method for estimating the distributional treatment effect that compares two potential outcome distributions for treated and control groups. Furthermore, we provide a nonparametric likelihood ratio test for the hypothesis that the two potential outcome distributions are identical. Second, we develop two methods for discovering effect modification in a matched observational study data: (1) the CART method and (2) the Submax method. Both methods are applied to real data examples for finding effect modifiers that alter the magnitude of the treatment effect. Lastly, we provide a causal definition of the malaria attributable fever fraction (MAFF) that has not been studied in the causal inference field, and propose a novel maximum likelihood method to account for fever killing effect and measurement errors.