We address hyperbole detection as a binary classification task, comparing rule-based methods, fine-tuned transformers (BERT, RoBERTa), and large language models (LLMs) in zero-shot and few-shot prompting (Gemini, LLaMA). Fine-tuned transformers achieved the best overall performance, with RoBERTa attaining an F1-score of 0.82. Rule-based methods performed lower (F1 = 0.58) but remain effective in constrained linguistic contexts. LLMs showed mixed results: zero-shot performance was variable, while few-shot prompting notably improved outcomes, reaching F1-scores up to 0.79 without task-specific training data. We discuss the trade-offs between interpretability, computational cost, and data requirements across methods. Our results highlight the promise of LLMs in low-resource scenarios and suggest future work on hybrid models and broader figurative language tasks.