Environmental odors are often composed of multiple types of odorants. However, it remains unclear how the mixtures of odorants are detected and processed in the olfactory system. Using in vivo calcium imaging of mouse olfactory bulb and olfactory epithelium, we show that odors produce not only excitatory but also inhibitory responses in olfactory sensory neurons (OSNs). Heterologous assays indicate that odorants can act as agonists to some but inverse agonists to other odorant receptors. We also demonstrate that responses to odor mixtures are extensively suppressed or enhanced in OSNs. When high concentrations of odors are mixed, widespread antagonism suppresses the overall response amplitudes and density. In contrast, a mixture of low concentrations of odors often produces synergistic effects and boosts the faint odor inputs. Thus, odor responses are extensively tuned by inhibition, antagonism, and synergy at the most peripheral level. These mechanisms may explain why the mixed odors are perceived as more than just a simple sum of their components.