The new trend of full-screen devices encourages us to position a camera behind a screen. Removing the bezel and centralizing the camera under the screen brings larger display-to-body ratio and enhances eye contact in video chat, but also causes image degradation. In this paper, we focus on a newly-defined Under-Display Camera (UDC), as a novel real-world single image restoration problem. First, we take a 4k Transparent OLED (T-OLED) and a phone Pentile OLED (P-OLED) and analyze their optical systems to understand the degradation. Second, we design a novel Monitor-Camera Imaging System (MCIS) for easier real pair data acquisition, and a model-based data synthesizing pipeline to generate UDC data only from display pattern and camera measurements. Finally, we resolve the complicated degradation using learning-based methods. Our model demonstrates a real-time high-quality restoration trained with either real or synthetic data. The presented results and methods provide good practice to apply image restoration to real-world applications.