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This is a survey of the closely related fields of taut submanifolds and Dupin submanifolds of Euclidean space. The emphasis is on stating results in their proper context and noting areas for future research; relatively few proofs are given. The important class of isoparametric submanifolds is surveyed in detail, as is the relationship between the two concepts of taut and Dupin. Also included is a brief introduction to submanifold theory in Lie sphere geometry, which is needed to state manydoi:10.1007/978-1-4757-4096-7_5 fatcat:grdjghfr75awvljajoyiptf5h4