Modern online advertising systems inevitably rely on personalization methods, such as click-through rate (CTR) prediction. Recent progress in CTR prediction enjoys the rich representation capabilities of deep learning and achieves great success in large-scale industrial applications. However, these methods can suffer from lack of exploration. Another line of prior work addresses the exploration-exploitation trade-off problem with contextual bandit methods, which are recently less studied in the industry due to the difficulty in extending their flexibility with deep models. In this paper, we propose a novel Deep Uncertainty-Aware Learning (DUAL) method to learn CTR models based on Gaussian processes, which can provide predictive uncertainty estimations while maintaining the flexibility of deep neural networks. DUAL can be easily implemented on existing models and deployed in real-time systems with minimal extra computational overhead. By linking the predictive uncertainty estimation ability of DUAL to well-known bandit algorithms, we further present DUAL-based Ad-ranking strategies to boost up long-term utilities such as the social welfare in advertising systems. Experimental results on several public datasets demonstrate the effectiveness of our methods. Remarkably, an online A/B test deployed in the Alibaba display advertising platform shows an 8.2% social welfare improvement and an 8.0% revenue lift.