Mediation analysis is often used to help explain the relationship between two variables in terms of an additional (mediating) variable. This line of research focuses on how to best do inference and confidence interval formation with both regression-based and latent variable mediation analysis models (e.g., structural equation models). Much of this work overlaps with situations where there is missing/nonnormal data, and includes extensive Monte Carlo simulations conducted on high performance computing clusters. Mediation analysis is a widely popular topic in psychology, and there is a pressing need for further integrating this work with how to test causal assumptions in research with quasi-experimental designs.