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Intelligent personal digital assistants (IPDAs), a popular real-life application with spoken language understanding capabilities, can cover potentially thousands of overlapping domains for natural language understanding, and the task of finding the best domain to handle an utterance becomes a challenging problem on a large scale. In this paper, we propose a set of efficient and scalable shortlisting-reranking neural models for effective large-scale domain classification for IPDAs. The shortlisting stage focuses on efficiently trimming all domains down to a list of k-best candidate domains, and the reranking stage performs a list-wise reranking of the initial k-best domains with additional contextual information. We show the effectiveness of our approach with extensive experiments on 1,500 IPDA domains.