Non-fungible token (NFT) trade has grown drastically over recent years. While scholarship on the technical aspects and potential applications of NFTs has been steadily increasing, less attention has been directed to the human perception of or attitudes toward this new type of digital asset. The aim of this research is to investigate what concerns are expressed in relation to non-fungible tokens by those who engage with NFTs on the social media platform Twitter. In this study, data was gathered through online social media data mining of NFT-related posts on Twitter. Two datasets (with 18,373 and 36,354 individual tweet records, respectively) were obtained. Topic modeling was used as a method of data analysis. Our results reveal 19 overall themes of concerns around NFTs as expressed on Twitter, which broadly fall into two categories: concerns about attacks and threats by third parties; and concerns about trading and the role of marketplaces. Overall, this study offers a better understanding of the expressions of concern, uncertainty, and the perception of possible barriers related to NFT trading. These findings contribute to theoretical insight and can, moreover, function as a basis for developing practical design and policy interventions.