In this paper, we present the first large-scale dataset for semantic Segmentation of Underwater IMagery (SUIM). It contains over 1500 images with pixel annotations for eight object categories: fish (vertebrates), reefs (invertebrates), aquatic plants, wrecks/ruins, human divers, robots, and sea-floor. The images are rigorously collected during oceanic explorations and human-robot collaborative experiments, and annotated by human participants. We also present a comprehensive benchmark evaluation of several state-of-the-art semantic segmentation approaches based on standard performance metrics. Additionally, we present SUIM-Net, a fully-convolutional deep residual model that balances the tradeoff between performance and computational efficiency. It offers competitive performance while ensuring fast end-to-end inference, which is essential for its use in the autonomy pipeline by visuallyguided underwater robots. In particular, we demonstrate its usability benefits for visual servoing, saliency prediction, and detailed scene understanding. With a variety of use cases, the proposed model and benchmark dataset open up promising opportunities for future research on underwater robot vision.