We look at the four main approaches to the afterlife in Judaism: The Underworld, Resurrection, The Good Place & The Bad Place, and Reincarnation. See below for the sources used.
I. Holy Hades - She’ol, or, The Underworld
(35) And all his sons and all his daughters rose up to comfort him; but he refused to be comforted; and he said: ‘I will go down to She’ol, to my son mourning.’ And his father wept for him.
(32) [...] and the earth opened its mouth and swallowed them up with their households, all Korah’s people and all their possessions. (33) They went down alive into She’ol, with all that belonged to them; the earth closed over them and they vanished from the midst of the congregation. (34) All Israel around them fled at their shrieks, for they said, “The earth might swallow us!”
(18) For Sh’eol cannot praise You, death cannot celebrate You; They that go down into the pit cannot hope for Your truth.
As a cloud fades away, so one that goes down to She’ol shall not come up.
II. Back from the Dead - Resurrection
(11) Then God said unto me: ‘Son of man, these bones are the whole house of Israel; behold, they say: Our bones are dried up, and our hope is lost; we are clean cut off. (12) Therefore prophesy, and say unto them: Thus says the Lord, God: Behold, I will open your graves, and cause you to come up out of your graves, O My people; and I will bring you into the land of Israel.
(19) Thy dead shall live, my dead bodies shall arise— Awake and sing, you that dwell in the dust— For your dew is as the dew of light, and the earth shall bring to life the spirits.
(2) And many of them that sleep in the dust of the earth shall awake, some to everlasting life, and some to reproaches and to everlasting abhorrence.
Sifrei Devarim 306:35 [2nd-3rd Century CE]
R. Simai [said]: There is no section in the Torah that does not deal with the resurrection, but we lack the strength to expound it.
Talmud Bavli Ketubot 111a:1-27 [4th-6th Century CE]
Rabbi El’azar said: The dead of the lands outside of Eretz Yisrael will not come alive and be resurrected in the future, as it is stated: “And I will set glory [tzvi] in the land of the living” (Ezekiel 26:20). This teaches that with regard to a land which contains ‘My desire’ [tzivyoni], its dead will come alive; however, with regard to a land which does not contain Tziyyon, i.e., outside of Eretz Yisrael, its dead will not come alive. [...] The Gemara asks: And according to the opinion of Rabbi El’azar, will the righteous outside of Eretz Yisrael not come alive at the time of the resurrection of the dead? Rabbi Ile’a said: They will be resurrected by means of rolling, i.e., they will roll until they reach Eretz Yisrael, where they will be brought back to life. Rabbi Abba Salla Rava strongly objects to this: Rolling is an ordeal that entails suffering for the righteous! Abayé said: Tunnels are prepared for them in the ground, through which they pass to Eretz Yisrael.
III. Gan Eden / Gei Hinnom - Heaven & Hell
Tosefta Sanhedrin 13:3 [1st-2nd Century CE]
Beit Shammai taught: There are three groups– one is destined for eternal life, another consigned to eternal ignominy and eternal abhorrence, while those whose deeds are balanced will go down to Gei Hinnom, but when they scream they will ascend from there and be healed.
Talmud Bavli Berakhot 57b:10 [4th-6th Century CE]
Three things are microcosms of the World-that-Is-Coming, and they are: Shabbat, a sunny day, and sexual intercourse
Talmud Bavli Berakhot 17a:12 [4th-6th Century CE]
Rav was wont to say: The World-that-Is-Coming is not like this world. In the World-that-Is-Coming there is no eating, no drinking, no procreation, no business negotiations, no jealousy, no hatred, and no competition. Rather, the righteous sit with their crowns upon their heads, enjoying the splendor of the Divine Presence.
Talmud Bavli Shabbat 152b:8 [4th-6th Century CE]
Rabba said to Rav Naḥman: What happens to the souls of mediocre people, who are neither righteous nor wicked? Rav Naḥman said to him: It is good that you asked me this question, for even if I were dead I would not have been able to tell you that! Sh’muel said as follows: These and those, the souls of the wicked and of the mediocre people, are handed over to Dumah, the angel in charge of spirits. But these, the souls of the mediocre people, have rest, and these, the souls of the wicked, do not have rest.
IV. Soul (Re)Cycling - Reincarnation
R’ Sa’adiah Gaon, Book of Beliefs and Opinions, vi. 8 [9th Century CE]
I have found certain people, who call themselves Jews, professing the doctrine of ... ‘transmigration of souls.’ Many of them would even go so far as to assert that the spirit of a human being might enter into the body of a beast or that of a beast into the body of a human being, and other such nonsense and stupidities!
Zohar I:186b [11th-12th Century CE]
As long as a person is unsuccessful in their purpose in this world, the Holy One, blessed be God, uproots them and replants them over and over again.
Zohar III:99b [11th-12th Century CE]
Truly, all souls, must undergo transmigration; but humanity does not perceive the ways of the Holy One, how the revolving scale is set up and people are judged every day at all time, and how they are brought up before the Tribunal, before they enter into this world and after they leave it. They do not even perceive the many transmigrations and the many mysterious works which the Holy One accomplishes with many naked souls, and how many naked spirits roam about, in the other world, without being able to enter within the veil of the King's Palace
R' Hayyim Vital, Sha'ar HaGilgulim, 8 [16th Century CE]
Regarding reincarnation of souls, why do souls reincarnate? There are various reasons why souls reincarnate: a) they have transgressed on a particular commandment of the Torah; b) To correct a commandment that was neglected and is lacking by them; and c) For the sake of others, to guide them and help them to correct.
R' Moshe Hayyim Luzzato, Derekh Hashem, 2:10 [18th Century CE]
There is a core principle which guides all the ways of the world - and this is that which the highest wisdom has arranged in order to increase [the chance of] success, as I have explained. For a single soul will come to this world many different times in many different bodies. Through this one is able to repair at one point that which was corrupted at another point - or to complete that which was left unfinished. And only at the end of all these transmigrations will the future judgement occur, and thus the soul will be judged on all that which transpired during all the incarnations in which it was transmigrated and all the circumstances of each.