My research focuses on nonparametric statistics motivated by problems in causal inference and time-to-event analysis. In many scientific settings, it is impossible, unethical, or cost-prohibitive to conduct a controlled experiment in which an exposure or treatment of interest is randomly assigned to units in a population. In such cases, researchers often turn to observational data, where the mechanism assigning the exposure is unknown, to attempt to assess causal effects. Nonparametric estimation of the statistical parameters that result from identifying causal effects with observational is often complicated. I use tools from classical nonparametric statistics, including kernel methods, as well as tools from modern statistical theory, including semiparametric efficiency theory and empirical process theory, to develop and analyze nonparametric estimators of these parameters. A common feature of the estimators I develop is the ability to perform valid statistical inference while using machine learning estimators of nuisance parameters. A particular focus of my research is continuous exposures, which arise in many scientific fields including vaccine trials, environmental epidemiology, and the study of air pollution. My primary applied areas of interest are public health, epidemiology, and biomedicine.