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This paper is a review of all methods that have been used in the literature for the solution of a very important and challenging set of problems, namely electromagnetic scattering from inlets, cavities, and open ducts. The techniques examined have been grouped together according to their fundamental principles, so that easy and direct comparisons among them are facilitated. The complexity and difficulty of the problems are clearly inferred from the very long list of references, which includes several very recent articles. The purpose of the paper is to highlight the advantages and limitations of the techniques invoked, draw useful conclusions, and trigger initiatives for future improved approaches to the topic.