Can a Muslim man marry a Christian or Jewish woman (Ahlul Kitab)?

Allah made this matter clear in Surah Al-Maidah (5:5): a Muslim man may marry a chaste Christian or Jewish woman, and this is one of the very few interfaith permissions Islam grants. But permission is not the same as recommendation. Scholars across all major madhabs express serious concerns about who raises the children, whose values fill the home, and whether the husband's own deen stays protected. Many contemporary scholars call this marriage highly discouraged in today's environment precisely because those risks are very real. As for a Muslim woman marrying a non-Muslim man, that door is completely closed by unanimous scholarly consensus, no exceptions. Allah knows best.