Feedback and buffering---the use of reservoirs of molecules to maintain molecular concentrations---are the primary mechanisms for robust regulation in biochemical processes. The universal principles behind their combined effect, however, have not been studied before. Here, we determine the fundamental forms of cooperation and tradeoff between buffering and feedback. We find that negative feedback regulates slow-changing components of time-varying signals, while buffering regulates fast-changing components, consistent with observations of both ATP and pH regulation. We further find that buffering stabilizes feedback and improves its effectiveness, but also introduces molecular noise. In addition, we show that rapid-acting buffering imparts negative derivative feedback, while slow-acting buffering can result in feedforward filtering of specific signals; both are control strategies widely used in technology. Finally, we discover an empirical cross-species relationship between feedback in glycolysis and ATP buffering that is consistent with our findings.