The validity of empirical research often relies upon the accuracy of self-reported behavior and beliefs. Yet, eliciting truthful answers in surveys is challenging especially when studying sensitive issues such as racial prejudice, corruption, and support for militant groups. List experiments have attracted much attention recently as a potential solution to this measurement problem. Many researchers, however, have used a simple difference-in-means estimator without being able to efficiently examine multivariate relationships between respondents' characteristics and their answers to sensitive items. Moreover, no systematic means exist to investigate role of underlying assumptions. We fill these gaps by developing a set of new statistical methods for list experiments. We identify the commonly invoked assumptions, propose new multivariate regression estimators, and develop methods to detect and adjust for potential violations of key assumptions. For empirical illustrations, we analyze list experiments concerning racial prejudice. Open source software is made available to implement the proposed methodology.