As Deep Learning (DL) is continuously adopted in many industrial applications, its quality and reliability start to raise concerns. Similar to the traditional software development process, testing the DL software to uncover its defects at an early stage is an effective way to reduce risks after deployment. According to the fundamental assumption of deep learning, the DL software does not provide statistical guarantee and has limited capability in handling data that falls outside of its learned distribution, i.e., out-of-distribution (OOD) data. Although recent progress has been made in designing novel testing techniques for DL software, which can detect thousands of errors, the current state-of-the-art DL testing techniques usually do not take the distribution of generated test data into consideration. It is therefore hard to judge whether the 'identified errors' are indeed meaningful errors to the DL application (i.e., due to quality issues of the model) or outliers that cannot be handled by the current model (i.e., due to the lack of training data). Tofill this gap, we take thefi rst step and conduct a large scale empirical study, with a total of 451 experiment configurations, 42 deep neural networks (DNNs) and 1.2 million test data instances, to investigate and characterize the impact of OOD-awareness on DL testing. We further analyze the consequences when DL systems go into production by evaluating the effectiveness of adversarial retraining with distribution-aware errors. The results confirm that introducing data distribution awareness in both testing and enhancement phases outperforms distribution unaware retraining by up to 21.5%.