Transformers have proved to be very effective for visual recognition tasks. In particular, vision transformers construct compressed global representations through self-attention and learnable class tokens. Multi-resolution transformers have shown recent successes in semantic segmentation but can only capture local interactions in highresolution feature maps. This paper extends the notion of global tokens to build GLobal Attention Multi-resolution (GLAM) transformers. GLAM is a generic module that can be integrated into most existing transformer backbones. GLAM includes learnable global tokens, which unlike previous methods can model interactions between all image regions, and extracts powerful representations during training. Extensive experiments show that GLAM-Swin or GLAM-Swin-UNet exhibit substantially better performances than their vanilla counterparts on ADE20K and Cityscapes. Moreover, GLAM can be used to segment large 3D medical images, and GLAM-nnFormer achieves new state-of-the-art performance on the BCV dataset.