Biblical theologians have many different, sometimes contradictory views of hell, with the Tanakh and New Testament giving justification for almost every last one of them. This can partly be sourced to shoddy translation. Hell was a term for the afterlife in some Germanic religions-it was the closest equivalent Germanic languages, such as early English, had for Sheol. For similar reasons, Sheol became Hades when the New Testament was translated into Greek. The New Testament also turns Gehenna to Armageddon, the bottomless pit to Tartarus and Abaddon to Apollyon. In English Hell was deemed good enough for these places nearly all the time, despite their differences, and for the most part continues to be used this way.
Sheol, the world of the dead, is an ancient Semite concept and though Mot, the Semitic god of death, was considered to be evil, Sheol was not a place where evil reigned nor a punishment for evil beings as hell is often thought to be, just an inevitability. The Tanakh is not much different, representing Sheol with imagery of subterranean graves, worms, maggots and moths: undesirable, but no association with Satan, fallen angels or fire. However, the Book of Job and the Psalms do compare the world of the dead to Abaddon, the place of destruction, which is described with fiery imagery. These two places are kept distinct in Hebrew, but this is partially where we get the idea of a fiery hell. Gehenna, a refuse dump where trash and dead bodies were often burnt, was a very Earthy place but it has also lent itself to the idea of fiery hell and coincidentally shares imagery with both Abaddon and Sheol, helping bridge them together.
Though it is not considered canon to most Jews or Christians today, references to the "first" book of Enoch can be found in the New Testament's Jude and it is in Enoch where the bottomless pit is most vividly described; a prison full of stars (compared to burning mountains, the Hebrews equated stars with Meteors) that continuously burn away the evil of angels too dangerous to be contained anywhere else. The New Testament's Luke also has spirits exercised by the Christ pleading not to be sent to this pit and Revelation has the servants of an angel named Abaddon released from the pit to punish wicked people on Earth. Revelation also tells that The Beast of the Sea will emerge from the pit and provoke mankind's final rebellion against God.
How Abaddon the angel relates to Abaddon the place is better left for another discussion but it is from the bottomless pit we connect hell to a prison for wicked spirits, fallen angels and punishment. None of the yet mentioned locals are said to be where human souls are punished specifically but that concept is still present in the Bible. The outer darkness of weeping and gnashing of teeth oft mentioned by Jesus of Nazareth in the gospels as well as the risk of going into life long Kolasis (Greek for correction or punishment) mentioned in the New Testament's Matthew are possible fates for humans though that may or may not be related to Abaddon, Sheol or The Pit. How they relate, if at all, is never made clear in the Bible however.
What is clear, at least according to Revelation, is that the world of the dead, Sheol, will not be eternal. Eventually all of those in it will be judged. Those who are judged unfavorably, refuse to admit their transgressions and do not repent for their wrong doing will not be allowed to leave it. They will forfeit life in the world to come, remaining dead and death itself shall be cast into a river of fire and sulfur which will serve as the second death, the new world of the dead. Some equate the river of fire to the aforementioned place of destruction but regardless, its influence on our ideals of hell are obvious, sulfur being more commonly known as brimstone.
One place the river of fire draws debate in theological interpretations (relevant to this analysis) is on it being purely punishment (the burning makes them suffer for their sins), benign separation (they are dead so they do not suffer) or reformative (there sins are merely burned away, as in Enoch)? Those arguing reformation would argue that sulfur was used in balms, fungicide, antiparasitics, fumigation and bleach. They would reference Matthew 5:13 and 9:49 arguing that everyone being "salted with fire" and relate the statement to salt's high melting point allowing one to separate impurities (sin) from salt (the soul) with fire. Those arguing simple punishment will point out sulfur is commonly found around volcanoes and would therefore be associated with God's wrath. The nigh unquenchable, rancid smelling, blue flames Sulfur gives off would further back up those who argue in favor of simple punishment. Finally Revelation states the world to come will have no sun, for God himself will provide light to all of those admitted into it. The idea of hell being merely separation from God comes from combining this with "The Outer Darkness Of Weeping And Gnashing Of Teeth". There is a constantly given measurement of time given for these events but not a clear one. In Hebrew the word olam implies for the age of the world which in Greek becomes aeon which literally means long and unspecified. Hell very well could be forever, as English translations usually state, but given what we know it does not necessarily have to be, which is the strongest argument for those insisting on reformation rather than plain punishment.
Outside of the Bible, the Talmuds entertain the idea of punishment in the grave for apostates. The Islamic Trinity's Jahannam, which also frequently translated as hell, leaves no room for doubt that disbelievers will be punished eternally in the most terrifying ways. Mahayana Buddhism teaches reincarnation but some schools have also taught of souls getting their bad karma burned away during the interregnum, similar to some more corrective views of hell. The concept is definitely not limited to the Tanakh or New Testament (which do not even have what was the completely unrelated word "hell" in their originally intended languages but this was type to give one a better idea of how hell came to be viewed how it is from the Bible. At least, to English speakers.
