Continual learning for segmentation has recently seen increasing interest. However, all previous works focus on narrow semantic segmentation and disregard panoptic segmentation, an important task with real-world impacts. In this paper, we present the first continual learning model capable of operating on both semantic and panoptic segmentation. Inspired by recent transformer approaches that consider segmentation as a mask-classification problem, we design CoMFormer. Our method carefully exploits the properties of transformer architectures to learn new classes over time. Specifically, we propose a novel adaptive distillation loss along with a mask-based pseudo-labeling technique to effectively prevent forgetting. To evaluate our approach, we introduce a novel continual panoptic segmentation benchmark on the challenging ADE20K dataset. Our CoMFormer outperforms all the existing baselines by forgetting less old classes but also learning more effectively new classes. In addition, we also report an extensive evaluation in the large-scale continual semantic segmentation scenario showing that CoMFormer also significantly outperforms state-of-the-art methods.