In this seminar I will present our paper that was published in NeurIPS 2024. We introduce hierarchical selective classification, which extends selective classification to a hierarchical setting. Our approach leverages the inherent structure of class relationships, enabling models to reduce the specificity of their predictions when faced with uncertainty. We formalize hierarchical risk and coverage, and introduce hierarchical risk-coverage curves. Next, we develop algorithms for hierarchical selective classification (which we refer to as "inference rules"), and propose an efficient algorithm that guarantees a target accuracy constraint with high probability. Lastly, we conduct extensive empirical studies on over a thousand ImageNet classifiers, revealing that training regimes such as CLIP, pretraining on ImageNet21k and knowledge distillation boost hierarchical selective performance.