Semantic Morphology addresses the problem of designing the rules needed for mapping between the semantic lexicon and semantic grammar. The text discusses the relation between semantics, lexicon, and morphology in unification-based grammars and builds on the current trends in Computational Semantics to use underspecification and compositionality. The approach to Semantic Morphology advocated here assumes compositional word formation from (semantic) word roots and affixes that are given their own entries in the semantic lexicon. Different feature usages are then utilized to reach the intended surface word-form matches, with the correct feature settings.