Product attribute extraction is an emerging field in information extraction and e-commerce, with applications including knowledge base construction, product recommendation, and enhancing customer experiences. In this work, we explore the use of generative models for product attribute extraction. We analyze their utility with hard and soft prompting methods, and demonstrate their ability to generate implicit attribute values, which state-of-the-art sequence tagging models are unable to extract. We perform a wide range of experiments on Amazon and MAVE product attribute datasets, and are the first to present results on multilingual attribute extraction. Our results show that generative models can outperform state- of-the-art tagging models for explicit product attribute extraction while having greater data efficiency, that they have the unique ability to perform implicit attribute extraction, and that in certain settings large language models can perform competitively with finetuned models with as little as two in-context examples.