Maimonides, answered from the texts and cited to the page.
The world to come is the existence of the cleansed soul through what it has apprehended in its lifetime — the intellect bound to the intelligibles it has come to know, the soul and its learning becoming one thing (Introduction to Pereq Heleq). It is not a place of eating, drinking, bathing, or sexual pleasure; it is not a celestial reward proportioned to halakhic punctiliousness; it is the natural continuation of a life devoted to knowledge of the Creator.
The sinner who has filled his life with bodily pleasure and ignored the intelligibles simply terminates at death — there is nothing of him to survive, and the talmudic image of Gehenna as the abode of post-mortem torment plays no systematic role in the world I describe.1 Resurrection of the dead — the thirteenth principle — is a real future miracle and not allegorical (this I defended in the Essay on Resurrection); but it is a temporary miracle, after which the resurrected die again, and the eternal world to come is then attained, and is the world of the cleansed intellect.234
In the world to come, there is no body or physical form, only the souls of the righteous alone, without a body, like the ministering angels. Since there is no physical form, there is neither eating, drinking, nor any of the other bodily functions of this world like sitting, standing, sleeping, death, sadness, laughter, and the like.Mishneh Torah, Repentance
Included in the twenty-four is "he who denies the Resurrection."? In connection with the world-to-come, to which I referred there, I clearly stressed that it was the ultimate goal.Epistles, pp. 62–63
This has also been explained in the Guide in my discussion of this world.'!® It occurs to me that what has made this people be in error about my views of the Resurrection is the difference in treatment. When I dealt with the world-to-come I dwelt at length and in detail on its description, elucidated its essence, and cited all the statements of the prophets and the sages that refer to it.Epistles, pp. 72–73
The Sages did not use the expression "the world to come" with the intention of implying that [this realm] does not exist at present or that the present realm will be destroyed and then, that realm will come into being. The matter is not so. Rather, [the world to come] exists and is present as implied by [Psalms 31:20: "How great is the good] that You have hidden...Mishneh Torah, Repentance
Genuinely held in both directions: immortality as intellectual apprehension is the doctrine of Mishneh Torah and Pereq Heleq; resurrection as literal future event is the principle defended against Samuel ben Eli's accusation and against the Yemenite questioners of 1185. Both are true, and the Essay on Resurrection explains how. The reconciliation is the temporary-resurrection doctrine — the dead rise, then die, then attain the world to come of the intellect. Halbertal raises the question whether resurrection is a necessary belief (Guide III:28: politically required for social order) rather than a true belief; my published position is that it is a true belief, defended in the Essay. The Essay is my answer; I do not retract it. The simple-believer problem cuts in here as well: the unlearned Jew who observes punctiliously without engaging the intelligibles will not have the intellectual apprehension that survives, and the implication is harsh. I hold the implication.