Deep learning models often fail to maintain their performance on new test domains. This problem has been regarded as a critical limitation of deep learning for real-world applications. One of the main causes of this vulnerability to domain changes is that the model tends to be biased to image styles (i.e. textures). To tackle this problem, we propose Style-Agnostic Networks (SagNets) to encourage the model to focus more on image contents (i.e. shapes) shared across domains but ignore image styles. SagNets consist of three novel techniques: style adversarial learning, style blending and style consistency learning, each of which prevents the model from making decisions based upon style information. In collaboration with a few additional training techniques and an ensemble of several model variants, the proposed method won the 1st place in the semi-supervised domain adaptation task of the Visual Domain Adaptation 2019 (VisDA-2019) Challenge.