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Mediation analysis is one of the most widely used statistical techniques in the social, behavioral, and medical sciences. Mediation models allow to study how an independent variable affects a dependent variable indirectly through one or more intervening variables, which are called mediators. The analysis is often carried out via a series of linear regressions, in which case the indirect effects can be computed as products of coefficients from those regressions. Statistical significance of the indirect effects is typically assessed via a bootstrap test based on ordinary least-squares estimates. However, this test is sensitive to outliers or other deviations from normality assumptions, which poses a serious threat to empirical testing of theory about mediation mechanisms. The R package robmed implements a robust procedure for mediation analysis based on the fast-and-robust bootstrap methodology for robust regression estimators, which yields reliable results even when the data deviate from the usual normality assumptions. Various other procedures for mediation analysis are included in package robmed as well. Moreover, robmed introduces a new formula interface that allows to specify mediation models with a single formula, and provides various plots for diagnostics or visual representation of the results.