Automatically associating social media posts with topics is an important prerequisite for effective search and recommendation on many social media platforms. However, topic classification of such posts is quite challenging because of (a) a large topic space (b) short text with weak topical cues, and (c) multiple topic associations per post. In contrast to most prior work which only focuses on post-classification into a small number of topics (10-20), we consider the task of large-scale topic classification in the context of Twitter where the topic space is 10 times larger with potentially multiple topic associations per Tweet. We address the challenges above and propose a novel neural model, that (a) supports a large topic space of 300 topics (b) takes a holistic approach to tweet content modeling – leveraging multi-modal content, author context, and deeper semantic cues in the Tweet. Our method offers an effective way to classify Tweets into topics at scale by yielding superior performance to other approaches (a relative lift of 20% in median average precision score) and has been successfully deployed in production at Twitter.