In this paper, deep learning-based techniques for film grain removal and synthesis that can be applied in video coding are proposed. Film grain is inherent in analog film content because of the physical process of capturing images and video on film. It can also be present in digital content where it is purposely added to reflect the era of analog film and to evoke certain emotions in the viewer or enhance the perceived quality. In the context of video coding, the random nature of film grain makes it both difficult to preserve and very expensive to compress. To better preserve it while compressing the content efficiently, film grain is removed and modeled before video encoding and then restored after video decoding. In this paper, a film grain removal model based on an encoder-decoder architecture and a film grain synthesis model based on a conditional generative adversarial network (cGAN) are proposed. Both models are trained on a large dataset of pairs of clean (grain-free) and grainy images. Quantitative and qualitative evaluations of the developed solutions were conducted and showed that the proposed film grain removal model is effective in filtering film grain at different intensity levels using two configurations: 1) a non-blind configuration where the film grain level of the grainy input is known and provided as input; and 2) a blind configuration where the film grain level is unknown. As for the film grain synthesis task, the experimental results show that the proposed model is able to reproduce realistic film grain with a controllable intensity level specified as input.