The question of how morphologically complex words (assign-ment, listen-ed) are represented and processed in the brain has been one of the most hotly debated topics in the cognitive neuroscience of language. Do complex words engage cortical representations and processes equivalent to single lexical objects or are they processed as sequences of separate morpheme-like units? Research on morphological processing has suggested that adults make efficient use of both lexical (i.e., whole word) storage and retrieval, as well as combinatorial computation in processing morphologically complex words. Psycholinguistic studies have demonstrated that processing of complex words can be affected both by properties of the morphemes and the whole words, such as their frequency, transparency, and regularity. Furthermore, this research has been informative about the time-course of complex word recognition and production, and the role of morphological structure in these processes. At the neural level, left-hemisphere inferior frontal and superior temporal areas, and negative-going event-related potentials, have been consistently associated with morphological processing. While most previous research has been done on the recognition of morphologically complex words in adult native speakers, much less is known about neurocognitive processes involved in the on-line production of morphologically complex words, and even less on morphological processing in children and non-native speakers. Moreover, we have limited understanding of how linguistically distinct morphological processes, e.g. inflectional (listen-ed) versus derivational (assign-ment), are handled by the cortical language networks. This e-book gives an up-to-date overview of the questions currently addressed in the field of morphological processing. It highlights the significance of morphological information in language processing, both written and spoken, as assessed by a variety of methods and approaches. It also points to a number of unresolved issues, and provides future directions for research in this key area of cognitive neuroscience of language.