The last 40 years have witnessed a growing interest in the mechanisms underlying the visual identification of complex words. A large amount of experimental data has been amassed, but although a growing number of studies are proposing explicit theoretical models for their data, no comprehensive theory has gained substantial agreement among scholars in the field. We believe that this is due, at least in part, to the presence of several controversial pieces of evidence in the literature and, consequently, to the lack of a well-defined set of experimental facts that any theory should be able to explain. With this review, we aim to delineate the state of the art in the research on the visual identification of complex words. By reviewing major empirical evidences in a number of different paradigms such as lexical decision, word naming, and masked and unmasked priming, we were able to identify a series of effects that we judge as reliable or that were consistently replicated in different experiments, along with some more controversial data, which we have tried to resolve and explain. We concentrated on behavioral and electrophysiological studies on inflected, derived, and compound words, so as to span over all types of complex words. The outcome of this work is an analytical summary of well-established facts on the most relevant morphological issues, such as regularity, morpheme position coding, family size, semantic transparency, morpheme frequency, suffix allomorphy, and productivity, morphological entropy, and morpho-orthographic parsing. In discussing this set of benchmark effects, we have drawn some methodological considerations on why contrasting evidence might have emerged, and have tried to delineate a target list for the construction of a new all-inclusive model of the visual identification of morphologically complex words.