Intimacy is an important social aspect of language. Computational modeling of intimacy in language could help many downstream applications like dialogue systems and offensiveness detection. Despite its importance, resources and approaches on modeling textual intimacy remain rare. To address this gap, we introduce MINT, a new Multilingual intimacy analysis dataset covering 13,372 tweets in 10 languages including English, French, Spanish, Italian, Portuguese, Korean, Dutch, Chinese, Hindi, and Arabic along with SemEval 2023 Task 9: Multilingual Tweet Intimacy Analysis. Our task attracted 45 participants from around the world. While the participants are able to achieve overall good performance on languages in the training set, zero-shot prediction of intimacy in unseen languages remains challenging. Here we provide an overview of the task, summaries of the common approaches, and potential future directions on modeling intimacy across languages. All the relevant resources are available at https: //sites.google.com/umich.edu/ semeval-2023-tweet-intimacy.