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This review focuses on material distribution-based topology optimization methods for boundary-effect-dominated problems. More precisely, it addresses problems where the behavior at or near the boundaries of the domain significantly influences the physics, such as problems involving boundary layers or the skin effect. While traditional topology optimization techniques have been highly successful in idealized settings, boundary-sensitive problems introduce unique challenges. We survey the historical development of relevant ideas, including fictitious-domain methods and filtering techniques, and provide a detailed account of modern approaches for handling boundary effects. Key topics include cascades of filters, multi-field representations, and methods for controlling length scale and interface sharpness. We also review specialized strategies for pressure and thermal loads, as well as recent advances in the design of coated structures and impedance-based modeling of boundary layers. This article aims to provide a comprehensive and structured overview of the field.