The rise of social media has offered a fast and easy way for the propagation of disinformation and conspiracy theories. Despite the research attention that has received, disinformation detection remains an open problem and users keep sharing texts that contain false statements. Several are the attempts of foreign information manipulation interference that our countries are exposed to. The European External Action Service (EEAS) and the European Digital Media Observatory (EDMO) are giving special importance to fight and analyse the disinformation narratives of this information warfare. Conspiracy theories are complex narratives that attempt to explain the ultimate causes of significant events as cover plots orchestrated by secret, powerful, and malicious groups. Their automatic detection in written texts has recently gained popularity although the problem is commonly framed as a binary classification task, which can be detailed more thoroughly with fine-grained approaches corresponding to multi-label or multi-class classifications. However, existing approaches do not distinguish between critical and conspiratorial thinking. This distinction has important implications for automatic content moderation: if models do not differentiate between critical and conspiratorial thinking, there is a high risk of pushing people toward conspiracy communities. After covering the above aspects, I will finilise my keynote describing the challenge that we organised at PAN 2024 on discriminating between conspiracy narratives and critical thinking.