Morphology, understood as internal structure of words, has always figured prominently in linguistic typology, and it is with the morphological classification of languages into “fusional,” “agglutinating,” and “isolating” proposed by the linguists and philosophers of the early 19th century that the advent of typology is often associated. However, since then typology has shifted its interests toward mapping the individual parameters of cross-linguistic diversity and looking for correlations between them rather than classifying languages into idealized “types” and to syntactically and semantically centered inquiries. Since the second half of the 20th century, morphology has been viewed as just one possible type of expression of meaning or syntactic function, often too idiosyncratic to yield to any interesting cross-linguistic let alone universal generalizations. Such notions as “flexive” or “agglutinating” have proven to be ill-defined and requiring revision in terms of more primitive logically independent and empirically uncorrelated parameters. Moreover, well-founded doubts have been cast upon such basic notions as “word,” “affix,” and the like, which have notoriously resisted adequate cross-linguistically applicable definitions, and the same has been the fate of still popular concepts like “inflection” and “derivation.” On the other hand, most theoretically oriented work on morphology, concerned with both individual languages and cross-linguistic comparison, has largely abandoned the traditional morpheme-based approaches of the American structuralists of the first half of the 20th century, shifting its attention to paradigmatic relations between morphologically relevant units, which themselves can be larger than traditional words. These developments suggest a reassessment of the basic notions and analytic approaches of morphological typology. Instead of sticking to crude and possibly misleading notions such as “word” or “derivation,” it is necessary to carefully define more primitive and empirically better-grounded notions and parameters of cross-linguistic variation in the domains of both syntagmatics and paradigmatics, to plot the space of possibilities defined by these parameters, and to seek possible correlations between them as well as explanations of these correlations or of the lack thereof.