Yearn for or long for mean you want something emotionally. Crave means you want it physically. Example: you may long for a companionship, travel, or peace of mind. You may crave a hot meal or a cold drink.

Hey ياسمين, 1) ''Yearn for'': it means ''to have a strong, often melancholy desire for someone or something'' E.g.: ''The sailors out at sea yearned for their families''. E.g.: ''He sat alone in his room, yearning for his mother.'' 2) ''Long for'': it is used to convey the same meaning of ''yearn for''. However, it holds the idea of a far greater desire, especially for something that is difficult or impossible to obtain. E.g.: ''I long for the carefree days of my youth''. E.g.: ''She longed for her old friends''. E.g.: ''Unlikely though it may be, I long for the day when we shall regain our human rights.'' 3) ''Crave (for)'': it also means ''to have a great desire for something''. However, it is rather focused upon something that you need urgently or that is related to one's appetite''. E.g.: ''They craved for an unforgettable adventure.'' E.g.: ''There may be certain times of day when smokers crave a cigarette''. Hope that helps!!! :)