A physical blocks world, despite its relative simplicity, requires (in fully interactive form) a rich set of functional capabilities, ranging from vision to natural language understanding. In this work we tackle spatial question answering in a holistic way, using a vision system, speech input and output mediated by an animated avatar, a dialogue system that robustly interprets spatial queries, and a constraint solver that derives answers based on 3-D spatial modeling. The contributions of this work include a semantic parser that maps spatial questions into logical forms consistent with a general approach to meaning representation, a dialogue manager based on a schema representation, and a constraint solver for spatial questions that provides answers in agreement with human perception. These and other components are integrated into a multi-modal human-computer interaction pipeline.