This article presents a comparative study of a subfield of morphology learning referred to as minimally supervised morphological segmentation . In morphological segmentation, word forms are segmented into morphs, the surface forms of morphemes. In the minimally supervised data-driven learning setting, segmentation models are learned from a small number of manually annotated word forms and a large set of unannotated word forms. In addition to providing a literature survey on published methods, we present an in-depth empirical comparison on three diverse model families, including a detailed error analysis. Based on the literature survey, we conclude that the existing methodology contains substantial work on generative morph lexicon-based approaches and methods based on discriminative boundary detection. As for which approach has been more successful, both the previous work and the empirical evaluation presented here strongly imply that the current state of the art is yielded by the discriminative boundary detection methodology.