We introduce and address the problem of ad hoc table retrieval: answering a keyword query with a ranked list of tables. This task is not only interesting on its own account, but is also being used as a core component in many other table-based information access scenarios, such as table completion or table mining. The main novel contribution of this work is a method for performing semantic matching between queries and tables. Specifically, we (i) represent queries and tables in multiple semantic spaces (both discrete sparse and continuous dense vector representations) and (ii) introduce various similarity measures for matching those semantic representations. We consider all possible combinations of semantic representations and similarity measures and use these as features in a supervised learning model. Using a purpose-built test collection based on Wikipedia tables, we demonstrate significant and substantial improvements over a state-of-the-art baseline.