Did Eliyahu die or not? The literal text implies that there was no physical death and he ascended with his body to the heavens. However, man, in his human, bodily state cannot cross the barrier into the heavenly world as God discussed with Moshe during the revelation at Horev. Various approaches are suggested by the commentators. 

Courtesy of the Virtual Beit Midrash, Yeshivat Har Etzion