BACKGROUND: Melanoma is an aggressive form of skin cancer in which tumor-infiltrating lymphocytes (TILs) are a biomarker for recurrence and treatment response. Manual TIL assessment is prone to interobserver variability, and current deep learning models are not publicly accessible or have low performance. Deep learning models, however, have the potential of consistent spatial evaluation of TILs and other immune cell subsets with the potential of improved prognostic and predictive value. To make the development of these models possible, we created the Panoptic Segmentation of nUclei and tissue in advanced MelanomA (PUMA) dataset and assessed the performance of several state-of-the-art deep learning models. In addition, we show how to improve model performance further by using heuristic postprocessing in which nuclei classes are updated based on their tissue localization. RESULTS: The PUMA dataset includes 155 primary and 155 metastatic melanoma hematoxylin and eosin-stained regions of interest with nuclei and tissue annotations from a single melanoma referral institution. The Hover-NeXt model, trained on the PUMA dataset, demonstrated the best performance for lymphocyte detection, approaching human interobserver agreement. In addition, heuristic postprocessing of deep learning models improved the detection of noncommon classes, such as epithelial nuclei. CONCLUSION: The PUMA dataset is the first melanoma-specific dataset that can be used to develop melanoma-specific nuclei and tissue segmentation models. These models can, in turn, be used for prognostic and predictive biomarker development. Incorporating tissue and nuclei segmentation is a step toward improved deep learning nuclei segmentation performance. To support the development of these models, this dataset is used in the PUMA challenge.