Metal implants and other high-density objects in patients introduce severe streaking artifacts in CT images, compromising image quality and diagnostic performance. Although various methods were developed for CT metal artifact reduction over the past decades, including the latest dual-domain deep networks, remaining metal artifacts are still clinically challenging in many cases. Here we extend the state-of-the-art dual-domain deep network approach into a quad-domain counterpart so that all the features in the sinogram, image, and their corresponding Fourier domains are synergized to eliminate metal artifacts optimally without compromising structural subtleties. Our proposed quad-domain network for MAR, referred to as Quad-Net, takes little additional computational cost since the Fourier transform is highly efficient, and works across the four receptive fields to learn both global and local features as well as their relations. Specifically, we first design a Sinogram-Fourier Restoration Network (SFR-Net) in the sinogram domain and its Fourier space to faithfully inpaint metal-corrupted traces. Then, we couple SFR-Net with an Image-Fourier Refinement Network (IFR-Net) which takes both an image and its Fourier spectrum to improve a CT image reconstructed from the SFR-Net output using cross-domain contextual information. Quad-Net is trained on clinical datasets to minimize a composite loss function. Quad-Net does not require precise metal masks, which is of great importance in clinical practice. Our experimental results demonstrate the superiority of Quad-Net over the state-of-the-art MAR methods quantitatively, visually, and statistically. The Quad-Net code is publicly available at https://github.com/longzilicart/Quad-Net .