Determining the semantic intent of web queries not only involves identifying their semantic class, which is a primary focus of previous works, but also understanding their semantic structure. In this work, we formally define the semantic structure of noun phrase queries as comprised of intent heads and intent modifiers. We present methods that automatically identify these constituents as well as their semantic roles based on Markov and semi-Markov conditional random fields. We show that the use of semantic features and syntactic features significantly contribute to improving the understanding performance.