Reasoning is now central to modern foundation models, but remains underdeveloped in the audio modality. Unlike text transcripts, audio contains not only words but also vocal cues, background events, and temporal patterns, all of which can be necessary for reliable inference. This survey presents the first dedicated synthesis of audio reasoning in multimodal foundation models. We formulate audio reasoning as reasoning-augmented generation grounded in acoustic evidence, distinguishing it from conventional audio understanding. We then organize existing work around two core settings: **Audio-to-Text reasoning**, where models infer textual answers from acoustic input, and **Audio-to-Speech reasoning**, where models reason before or during speech generation under latency constraints. Finally, we summarize evaluation practices and challenges in acoustic grounding, shortcut learning, modality hallucination, and latency-constrained interaction.