Emotion Recognition (ER) is the process of identifying human emotions from given data. Currently, the field heavily relies on facial expression recognition (FER) because facial expressions contain rich emotional cues. However, it is important to note that facial expressions may not always precisely reflect genuine emotions and FER-based results may yield misleading ER. To understand and bridge this gap between FER and ER, we introduce eye behaviors as an important emotional cues for the creation of a new Eye-behavior-aided Multimodal Emotion Recognition (EMER) dataset. Different from existing multimodal ER datasets, the EMER dataset employs a stimulus material-induced spontaneous emotion generation method to integrate non-invasive eye behavior data, like eye movements and eye fixation maps, with facial videos, aiming to obtain natural and accurate human emotions. Notably, for the first time, we provide annotations for both ER and FER in the EMER, enabling a comprehensive analysis to better illustrate the gap between both tasks. Furthermore, we specifically design a new EMERT architecture to concurrently enhance performance in both ER and FER by efficiently identifying and bridging the emotion gap between the two.Specifically, our EMERT employs modality-adversarial feature decoupling and multi-task Transformer to augment the modeling of eye behaviors, thus providing an effective complement to facial expressions. In the experiment, we introduce seven multimodal benchmark protocols for a variety of comprehensive evaluations of the EMER dataset. The results show that the EMERT outperforms other state-of-the-art multimodal methods by a great margin, revealing the importance of modeling eye behaviors for robust ER. To sum up, we provide a comprehensive analysis of the importance of eye behaviors in ER, advancing the study on addressing the gap between FER and ER for more robust ER performance.