In this paper we introduce Mandarin language understanding methods developed for spoken language applications. We describe a set of strategies to improve the parsing performance for Mandarin. We also discuss two context resolution techniques adopted to handle Chinese ellipsis in a practical Mandarin spoken dialogue system. Experimental evaluation verifies the effectiveness and efficiency of our proposed parsing enhancements, in terms of both parse coverage and speed. System evaluation with human subjects also verifies the effectiveness of our proposed approaches to speech understanding and context resolution in practical conversational systems.