Grammars of signed languages tend to be based on grammars established for written languages, particularly the written language in use in the surrounding hearing community of a sign language. Such grammars presuppose categories of discrete elements which are combined into various sorts of structures. Recent analyses of signed languages go beyond this tradition, attending to "gradient" elements of signs and to the communicative and physical settings in which signs are produced. Important new insights are gained when sign language linguists consider such factors, making use of new tools of cognitive linguistics. A typological approach to signed languages suggests that they are of the opposite type to the surrounding spoken/written languages of Europe, North America, and East Asia. Those languages are dependent-marked, whereas signed languages are head-marked. (Contains 2 tables.)