This paper presents a novel unsupervised domain adaptation framework, called Synergistic Image and Feature Adaptation (SIFA), to effectively tackle the problem of domain shift. Domain adaptation has become an important and hot topic in recent studies on deep learning, aiming to recover performance degradation when applying the neural networks to new testing domains. Our proposed SIFA is an elegant learning diagram which presents synergistic fusion of adaptations from both image and feature perspectives. In particular, we simultaneously transform the appearance of images across domains and enhance domain-invariance of the extracted features towards the segmentation task. The feature encoder layers are shared by both perspectives to grasp their mutual benefits during the end-to-end learning procedure. Without using any annotation from the target domain, the learning of our unified model is guided by adversarial losses, with multiple discriminators employed from various aspects. We have extensively validated our method with a challenging application of crossmodality medical image segmentation of cardiac structures. Experimental results demonstrate that our SIFA model recovers the degraded performance from 17.2% to 73.0%, and outperforms the state-of-the-art methods by a significant margin.