Robust Bayesian analysis is the study of the sensitivity of Bayesian answers to uncertain inputs. This paper seeks to provide an overview of the subject, one that is accessible to statisticians outside the field. Recent developments in the area are also reviewed, though with very uneven emphasis. The topics to be covered include (i) The Development of Inherently Robust Procedures, including Use of Flat-tailed Distributions, Noninformative and Partially Informative Priors, and Nonparametric Bayes Procedures; (ii) Diagnostics, Influence, and Sensitivity; (iii) Global Robustness, involving Parametric and Nonparametric Classes of Priors and Likelihoods; (iv) Computation; (v) Interactive Elicitation; and (vi) Future Directions. Postscript File (639kB)