In this paper we provide a framework to reason about limited awareness of the action space in finitely repeated games. Our framework is rich enough to capture the full strategic aspect of limited awareness in a dynamic setting, taking into account the possibility that agents might want to reveal or conceal actions to their opponent or that they might become "aware of unawareness" upon observing non rationalizable behavior. We show that one can think of these situations as a game with incomplete information, which is fundamentally different, though, from the standard treatment of repeated games with incomplete information. We establish conditions on the "level of mutual awareness" of the action space needed to recover Nash and subgame perfect Nash equilibria from the standard theory with common knowledge. We also show that the set of sustainable payoffs in games with folk theorems does not relate in a monotone way to the "level of mutual awareness".