  This paper provides an overview of results and concepts in minimax robust
hypothesis testing for two and multiple hypotheses. It starts with an
introduction to the subject, highlighting its connection to other areas of
robust statistics and giving a brief recount of the most prominent
developments. Subsequently, the minimax principle is introduced and its
strengths and limitations are discussed. The first part of the paper focuses on
the two-hypothesis case. After briefly reviewing the basics of statistical
hypothesis testing, uncertainty sets are introduced as a generic way of
modeling distributional uncertainty. The design of minimax detectors is then
shown to reduce to the problem of determining a pair of least favorable
distributions, and different criteria for their characterization are discussed.
Explicit expressions are given for least favorable distributions under three
types of uncertainty: $\varepsilon$-contamination, probability density bands,
and $f$-divergence balls. Using examples, it is shown how the properties of
these least favorable distributions translate to properties of the
corresponding minimax detectors. The second part of the paper deals with the
problem of robustly testing multiple hypotheses, starting with a discussion of
why this is fundamentally different from the binary problem. Sequential
detection is then introduced as a technique that enables the design of strictly
minimax optimal tests in the multi-hypothesis case. Finally, the usefulness of
robust detectors in practice is showcased using the example of ground
penetrating radar. The paper concludes with an outlook on robust detection
beyond the minimax principle and a brief summary of the presented material.
