Jews do believe in an afterlife, but what this looks like is vague, according to the various texts. There are hints as to what happens (the good shall be reunited with their loved ones, the wicked excluded) but there aren't any specifics. This isn't an oversight, it's fundamental to the religion. The Torah and related texts are instructions for this life, not rulebooks on how to get into the next, better life.

Scholars debate why this is and I don't have a great answer except this general idea: religions suit the societies that create them. Jews wanted their people focused on the present. Christians wanted their people looking to the future.

Actually, the Christian texts don't have a lot to say about heaven or hell. Heaven is good, Hell is bad (and hot). Most of our modern ideas of both came from the Medieval period and are largely inventions of artists and writers, not theologians or priests.

I studied religion for my undergrad. One of those classes that I took was Ancient Israelite Religion, and in it, we discussed the ancient Israelite view of the afterlife. It's been a while since I've taken that class, so take this comment with a grain of salt.

The ancient Israelites (and some Jews still to this day, I think) didn't really believe in heaven or hell, per se. Their idea of the afterlife was basically that you die and you get to rest. It's comparable to the Greek idea of Hades. Souls go there and just...do nothing. A great verse is in Ecclesiastes 9:11:

Whatever your hand finds to do, do it with all your might; for there is no activity or planning or knowledge or wisdom in Sheol where you are going.

As I recall, this is one of the few mentions of an afterlife in the Old Testament at all, and it sounds pretty vague about what actually happens there. It's definitely not heaven or hell, because there's neither joy nor suffering. It's just a place of nothing.

That's the basic gist of it. I'm no expert, but that's pretty much what we learned from our professor who specialized in ancient Israelite studies. In short, they didn't believe in the devil as we know him (kind of related to your question), and their ideas of heaven and hell were either:

A. Not really discussed in the Bible

B. Not fully fleshed out yet

C. Didn't exist, and the afterlife wasn't central to their faith.

If Ecclesiastes is to be trusted, their belief structure would have focused more on one's life than what happens afterward. "Enjoy your work and toil because afterwards you get She'ol." Not bad, but nothing to really look forward to.

You might want to also crosspost the qustion to /r/ELINT (Explain Like I'm Not a Theologian).

/u/chromedizzle did a great summary. Most of what Judaism has on afterlife is the Pauline literature. However, different regions of Judaism had slightly different beliefs.

In one study on the matter, it writes: "Now one common approach used in several works on Greco-Roman conceptions of afterlife is the supposition of a gradual development of belief, from the most primitive belief in a continued existence in the grave, to the ascent of the soul to the stars. Without necessarily accepting the details of this approach, this is the organizing principle adopted in the present study."

Throughout the Mediterranean world, it's a little bit more thematic: "a 'subterranean' or 'downward' a conception of afterlife, in which the deceased is thought to exist perpetually in the grave or in the underworld."

But there are also "upward" conceptions of afterlife: "Somewhat analogous to (but not parallel with)... located between these two parts, it's been an examined formulae involving the term 'peace,' for example, the wish 'in peace be your sleep.'"

However, there is some expressions of resurrection belief in Jewish inscriptions. The Latin epitaph of Regina, found in Monteverde catacomb of Rome has one such example. It states (in English), "She will live again, return to the light again. For she can hope therefore that she may rise into the age promised for both the worth and the pious, she, a true pledge, who deserved to have an abode in the venerable country." This "return to the light" is up to interpretation. The tomb literally writes: "reditura ad lumina rursum" indicating that it's from under the earth, where there is no light.

Generally, however, it appears that most Jews just simply believed death was an everlasting peaceful rest.

Source:

Park, Joseph S. Conceptions of afterlife in Jewish inscriptions: with special reference to Pauline literature. Vol. 121. Mohr Siebeck, 2000.