Emotion Recognition (ER) is the process of analyzing and identifying human emotions from sensing data. Currently, the field heavily relies on facial expression recognition (FER) because visual channel conveys rich emotional cues. However, facial expressions are often used as social tools rather than manifestations of genuine inner emotions. To understand and bridge this gap between FER and ER, we introduce eye behaviors as an important emotional cue and construct an Eye-behavior-aided Multimodal Emotion Recognition (EMER) dataset. To collect data with genuine emotions, spontaneous emotion induction paradigm is exploited with stimulus material, during which non-invasive eye behavior data, like eye movement sequences and eye fixation maps, is captured together with facial expression videos. To better illustrate the gap between ER and FER, multi-view emotion labels for mutimodal ER and FER are separately annotated. Furthermore, based on the new dataset, we design a simple yet effective Eye-behavior-aided MER Transformer (EMERT) that enhances ER by bridging the emotion gap. EMERT leverages modality-adversarial feature decoupling and a multitask Transformer to model eye behaviors as a strong 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. Our EMER dataset and the trained EMERT models will be publicly available at https://github.com/kejun1/EMER.