This article presents a systematic exposition of how the basic ideas of Construction Grammar (CxG) (Goldberg, 2006) and the Parallel Architecture (PA) of grammar (Jackendoff, 2002]) provide the framework for a proper account of morphological phenomena, in particular word formation. This framework is referred to as Construction Morphology (CxM). As to the implications of CxM for the architecture of grammar, the article provides evidence against a split between lexicon and grammar, in line with CxG. In addition, it shows that the PA approach makes it possible to be explicit about what happens on which level of the grammar, and thus to give an insightful account of interface phenomena. These interface phenomena appear to require that various types of information are accessible simultaneously, and it is argued that constructional schemas have the right format for expressing these mutual dependencies between different types of information.