Heaven and Hell
Heaven and Hell have both been created and are currently in existence, as evidenced by verses of the Qur’an.
“It (Heaven) has been prepared for the pious.” [Qur’an, 3:133]
“Guard yourselves against the fire which has been prepared for the disbelievers.” [Qur’an, 3:131]
There are different levels in Heaven.
“And for each, there are ranks based on what they did.” [Qur’an, 6:132]
“Those who believe, and whose offspring follow them in faith, We shall unite their offspring with them, and We shall not cause decrease the reward of their deeds at all.” [Qur’an, 52:21] Ibn `Abbas said, “Allah will elevate the offspring of the believer, even if they were beneath him in deeds, in order that his eye might delight in them.” [Narrated by Tabari and Bazzar]
“Indeed, in Heaven there are one hundred levels which Allah has prepared for those who strive in His path, [the difference] between each [successive] level is like that between the sky and the earth. Therefore, when you ask Allah, then ask Him for al-Firdaws, for it is the highest [part] of Heaven, and the best [part] of Heaven. From it gush the rivers of Heaven, and above it is the `Arsh of the Most Gracious.” [Narrated by Bukhari and Muslim]
Heaven is the place of eternal enjoyment.
“Therein is that which the souls desire, and the eyes delight in.” 
“Indeed, the lowest place of one of you in Heaven is that he will be told, “Wish!” and then he will wish, and wish. Then, he will be asked, “Have you wished?” whereupon he will say, “Yes.” Then, he will be told, “Then indeed, for you is what you wishes, and the like of it along with it.” [Narrated by Ahmad]
“. . . . There is no disagreement between them, nor mutual hatred; their hearts are all like a single heart. They glorify Allah morning and evening.” [Narrated by Bukhari, Muslim, Ahmad, Tirmidhi]
“A caller will call : Indeed, for you is to live, so that you will never die. For you is to be healthy, so that you will never be sick; and to be young, so that you will never grow old. And indeed, for you is to receive delight, so that you will never be grieved. [Narrated by Muslim, Tirmidhi, Ahmad]
The Messenger of Allah (may Allah bless him and his Household and grant them peace) said : Allah, he Flawless, the Exalted, said : “I have prepared for My righteous servants what no eye has seen, nor any ear has heard, nor has occurred to the heart of a mortal.” [Narrated by Bukhari, Muslim, Tirmidhi, Ibn Majah]
“And a soul knows not what is concealed for them of the delight of the eye, as a recompense for what they used to do.” [Qur’an, 32:17]
The greatest of pleasures for the People of Heaven is seeing Allah.
“You shall see your Lord… and you will not be harmed by seeing Him. So if you can, do not let yourselves be overpowered in case of prayer observed before the rising of the sun and its setting.” [Narrated by Muslim, Bukhari]
“Celebrate the praise of your Lord before the rising of the sun and before its setting.” Q[20:130]
On the authority of Suhayb : The Messenger of Allah recited, (the words meaning), “For those who do good there is the best, and an addition.” [Yunus, 26] He said, “When the people of Heaven have entered Heaven and the People of Hell Hell, a caller will call, “O People of Heaven! Indeed, you have a promise with Allah which He desires to carry out.” They will say, “What is this promised thing? Has He not made our scales heavy, brightened our faces, entered us into Heaven and protected us from the Fire?” He said : Then, the veil will be lifted [from their eyes], and they will look at the Countenance of Allah, the Mighty, the Majestic.” He said, “And they were not given anything more beloved than looking at Him.” [Narrated by Muslim]
“Hell will be brought forth on that day, with seventy thousand reins, with each rein seventy thousand angels pulling it.” [Narrated by Muslim]
Hell is the place of eternal misery and punishment for the unbelievers. (Sinful Muslims will eventually emerge from it, however, as we have mentioned.) Its horrors are terrifying and unending.
“The fire of the Children of Adam, which you kindle, is one seventieth part of the fire of Jahannam.” [Narrated by Bukhari, Muslim, Malik]
Abu Hurayrah said, “Do you consider it to be red like this fire of yours which you kindle? Indeed, it is blacker than pitch.” [Narrated by Malik]
“Indeed, Jahannam is [prepared as] an ambush! A destination for the transgressors; abiding therein for [infinite] ages. They do not taste therein cold, nor [any] drink; except boiling water and a foul-smelling, intensely cold fluid; a fitting recompense.” [Qur’an, 78:21-26]
“The lightest of the People of the Fire in punishment on the Day of Resurrection will be a man in the hollows under whose feet shall be placed two coals on account of which his brain will boil. He does not consider that anyone has a more severe punishment than himself, although he is the lightest of them in punishment.” [Narrated by Bukhari and Muslim]
“Indeed, the hypocrites shall be in the lowest depths of the Fire, and you will never find for them any helper.” [Qur’an, 4:145]
Ibn `Abbas said, “[they will be] in caskets, bolted over them.” Abu Hurayrah said, “In caskets with doors which will be closed over them, and then they will be kindled from beneath them and from above them.” [Tafsir Ibn Kathir]
Eternality of Heaven and Hell
The Qur’an states clearly that neither nor Hell shall ever perish or pass away. The believers will continue to have bliss and enjoyment in Heaven, and the disbelievers will continue to be punished in Hell, without end.
“Those who believe and do good deeds, We shall enter them into gardens beneath which flow rivers, in which they shall abide forever.” [Qur’an, 4:57]
“Allah has cursed the disbelievers and has prepared for them a blazing fire, wherein they shall abide forever.” [Qur’an, 33:64-65]
And, in the authentic hadith, the Prophet (may Allah bless him and grant him peace) tells us, “Death will be brought [in the form of] a black-marked white ram and made to stand between the Garden (of Heaven) and the Fire (of Hell) . . . . and then it will be slaughtered, and it will be said, ‘Immortality, and no death [anymore]!'” [Narrated by Bukhari, Muslim, Ahmad, Nasa’i and Darimi]
“O Allah! We ask You for Your Pleasure and Heaven, and We seek refuge with You from Your wrath and the Fire.”