The morphological machinery of a language is at the service of syntax, but the service can be poor. A request may result in the wrong item (deponency), or in an item the syntax already has (syncretism), or in an abundance of choices (inflectional classes or morphological allomorphy). Network Morphology regulates the service by recreating the morphosyntactic space as a network of information sharing nodes, where sharing is through inheritance, and inheritance can be overridden to allow for the regular, irregular, and, crucially, the semiregular. The network expresses the system; the way the network can be accessed expresses possible deviations from the systematic. And so Network Morphology captures the semi-systematic nature of morphology. The key data used to illustrate Network Morphology are noun inflections in the West Slavonic language Lower Sorbian, which has three genders, a rich case system and three numbers. These data allow us to observe how Network Morphology handles inflectional allomorphy, syncretism, feature neutralization, and irregularity. Latin deponent verbs are used to illustrate a Network Morphology account of morphological mismatch, where morphosyntactic features used in the syntax are expressed by morphology regularly used for different features. The analysis points to a separation of syntax and morphology in the architecture of the grammar. An account is given of Russian nominal derivation which assumes such a separation, and is based on viewing derivational morphology as lexical relatedness. Areas of the framework receiving special focus include default inheritance, global and local inheritance, default inference, and orthogonal multiple inheritance. The various accounts presented are expressed in the lexical knowledge representation language DATR, due to Roger Evans and Gerald Gazdar.