Morphology, by its very language-specific nature, poses conceptual, methodological, and empirical problems for both linguistic theory and language typology. This chapter offers an overview of major issues in morphological typology, starting with the controversial definitions of basic notions such as ‘wordform’ and ‘lexeme’, and proceeding to the classification of morphological phenomena along the syntagmatic and paradigmatic axes. It is argued that traditional dichotomies such as ‘inflection’ vs. ‘derivation’ or ‘agglutination’ vs. ‘flexion’ are to by replaced by multidimensional classifications based on a broad empirical coverage of morphological phenomena attested in human languages, and that only through a mutually informed fruitful interaction of typologists and morphological theorists can an adequate cross-linguistically valid and analytically sophisticated model of morphology be attained.