This thesis presents advances in statistical causal modeling and inference. The first part uncovers hidden assumptions in statistical causal discovery. We find that, in many widely used benchmarking configurations, implicit assumptions tend to make variables increasingly predictable along the causal order. This is at odds with a supposedly stochastic model class, and can render causal discovery nearly trivial in large graphs. We introduce a new measure to diagnose the presence and strength of this pattern. The second part suggests a temporal interpretation of causal graphs. We argue that, under the assumption that causes precede effects, edges can only relate variables unambiguously if their temporal relation is specified. We provide a formalism to capture a notion of time for causal variables and their aggregations, and discuss implications for statistical causality. The third part provides new methodology for estimating conditional densities that promise more precise causal effect estimation. Our approach transforms conditional density estimation into a single nonparametric regression task, which allows the use of powerful regression methods that work well even in high dimensions. By deriving auxiliary samples from a set of given observations, our approach overcomes problems of overfitting that have constrained previous approaches. We prove convergence in the data limit, provide an efficient implementation, and demonstrate the promise of our method on two large real-world datasets.