Memes are becoming increasingly more popular in online media, especially in social networks. They usually combine graphical representations (images, drawings, animations or video) with text to convey powerful messages. In order to extract, process and understand the messages, AI applications need to employ multimodal algorithms. In this paper, we introduce a curated dataset of real memes in the Romanian language, with multiple annotation levels. Baseline algorithms were employed to demonstrate the usability of the dataset. Results indicate that further research is needed to improve the processing capabilities of AI tools when faced with Internet memes.