Bava Basra 15a-b lists a number of opinions as to when Iyov lived:
- R' Levi bar Chama: In the days of Moshe
- Rava: In the days of the Meraglim
- Unnamed student of R' Shmuel bar Nachmani: Iyov never lived; it's entirely a mashal
- R' Yochanan and Rav Elazar: Beginning of Bayis Sheini
- Simple understanding of an unattributed Braisa: During Galus Mitzraim
- R' Eliezer: In the days of Sefer Rus
- R' Yehoshua ben Karchah: In the days of Achashveirosh
- R' Nassan: In the days of the kingdom of Sheva
- Chachamim: In the days of the Kasdim (i.e. Nevuchadnetzar - Rashi)
- Yeish Omrim: In the days of Yaakov
The Gemara ibid. quotes a Braisa that Sefer Iyov was written by Moshe Rabbeinu; this opinion can only hold according to R' Levi bar Chama, Rava, the student of R' Shmuel bar Nachmani, the unattributed Braisa, and Yeish Omrim. According to the remaining six opinions, Iyov lived after Moshe.
According to these opinions, who wrote Sefer Iyov?