Deep learning (DL) has greatly advanced audio classification, yet the field is limited by the scarcity of large-scale benchmark datasets that have propelled progress in other domains. While AudioSet is a pivotal step to bridge this gap as a universal-domain dataset, its restricted accessibility and limited range of evaluation use cases challenge its role as the sole resource. Therefore, we introduce BirdSet, a large-scale benchmark dataset for audio classification focusing on avian bioacoustics. BirdSet surpasses AudioSet with over 6,800 recording hours ($\uparrow\!17\%$) from nearly 10,000 classes ($\uparrow\!18\times$) for training and more than 400 hours ($\uparrow\!7\times$) across eight strongly labeled evaluation datasets. It serves as a versatile resource for use cases such as multi-label classification, covariate shift or self-supervised learning. We benchmark six well-known DL models in multi-label classification across three distinct training scenarios and outline further evaluation use cases in audio classification. We host our dataset on Hugging Face for easy accessibility and offer an extensive codebase to reproduce our results.