Natural language understanding is a sub-field of natural language processing, which builds automated systems to understand natural language. It is such an ambitious task that it sometimes is referred to as an AI-complete problem, implying that its difficulty is equivalent to solving the central artificial intelligence problem -- making computers as intelligent as people. Despite its complexity, natural language understanding continues to be a fundamental problem in natural language processing in terms of its theoretical and empirical importance. In recent years, startling progress has been made at different levels of natural language processing tasks, which provides great opportunity for deeper natural language understanding. In this thesis, we focus on the task of semantic parsing, which maps a natural language sentence into a complete, formal meaning representation in a meaning representation language. We present two novel state-of-the-art learned syntax-based semantic parsers using statistical syntactic parsing techniques, motivated by the following two reasons. First, the syntax-based semantic parsing is theoretically well-founded in computational semantics. Second, adopting a syntax-based approach allows us to directly leverage the enormous progress made in statistical syntactic parsing. The first semantic parser, Scissor, adopts an integrated syntactic-semantic parsing approach, in which a statistical syntactic parser is augmented with semantic parameters to produce a semantically-augmented parse tree (SAPT). This integrated approach allows both syntactic and semantic information to be available during parsing time to obtain an accurate combined syntactic-semantic analysis. The performance of Scissor is further improved by using discriminative reranking for incorporating non-local features. The second semantic parser, SynSem, exploits an existing syntactic parser to produce disambiguated parse trees that drive the compositional semantic interpretation. This pipeline approach allows semantic parsing to conveniently leverage the most recent progress in statistical syntactic parsing. We report experimental results on two real applications: an interpreter for coaching instructions in robotic soccer and a natural-language database interface, showing that the improvement of Scissor and SynSem over other systems is mainly on long sentences, where the knowledge of syntax given in the form of annotated SAPTs or syntactic parses from an existing parser helps semantic composition. SynSem also significantly improves results with limited training data, and is shown to be robust to syntactic errors. / text