This article investigates the automatic generation of irony explanations in English and Dutch tweets. We begin by developing and validating a conceptual framework through a pilot study on English data. Our evaluation confirms that both fine-tuned open-source models (Llama 3) and proprietary models (GPT-4) can produce high-quality explanations in English, effectively incorporating relevant world knowledge. While proprietary models also perform well on Dutch data, smaller open-source models face challenges in adapting to this less-resourced language. Despite these limitations, we find that state-of-the-art models in both languages generate effective irony explanations, hence facilitating a deeper linguistic analysis of world knowledge involved in understanding irony on social media. Our analysis revealed that while models can already produce world knowledge about specific people, organizations, and events, their explanations are sometimes overly verbose, inadequate or focused too much on less relevant world knowledge.