This paper investigates the view update problem for XML views published from relational data. We consider (possibly) recursively defined XML views, compressed into DAGs and stored in relations. We provide new techniques to efficiently support XML view updates specified in terms of XPath expressions with recursion and complex filters. The interaction between XPath recursion and DAG compression of XML views makes the analysis of XML view updates intriguing. Furthermore, many issues are still open even for relational view updates, and need to be explored. In response to these, on the XML side, we revise the update semantics to accommodate XML side effects based on the semantics of XML views, and present efficient algorithms to translate XML updates to relational view updates. On the relational side, we propose a mild condition on SPJ views, and show that under this condition the analysis of deletions on relational views becomes PTIME while the insertion analysis is NP-complete. We develo...