There are two kinds of Hollow Earth theories: Concave Hollow Earth theories and Convex Hollow Earth theories. Convex Hollow Earth theories state that the surface of the planet we live on is the external surface of an hollow planet. Concave Hollow Earth theories state that we and all the universe are inside a hollow planet.
According to Newton's Law of Gravity, the gravitational force is actually zero inside a spherical hollow shell of matter (absent other masses). Thus, even if the Earth were hollow, someone on the inside would not be pulled outwards or be able to stand on the inner surface, as is popularly supposed; rather, they would be weightless (with some slight residual gravity arising from the fact that the Earth is not perfectly spherical). (The centrifugal force from the Earth's rotation would pull a person outwards, but even at the equator this force is only 0.3% of ordinary Earth gravity.)
In 1818, John Cleves Symmes, Jr suggested that the Earth was actually a hollow shell about 800 miles thick, with openings at both poles about 1400 miles across. With charming naivete he proposed calling the "inner lands" Symzonia.
Other writers have proposed that subterranean caverns or a hollow Earth are the abodes of "ascended masters" of esoteric wisdom. Antarctica, the North Pole, Tibet, Peru, and Mount Shasta in California, USA, have all been suggested as the locations of entrances to these subterranean realms, with some advancing the theory that these places are the actual homeland of UFOs.
The most popular of these theories (in the US, at least) was promoted from 1945-49 as "the Shaver Mystery" in the pages of the science fiction pulp magazine "Amazing Stories." The magazine's editor Ray Palmer ran series of stories by Richard Sharpe Shaver, claiming they were factual, though presented as fiction. Shaver claimed the earth was honeycombed with caves that had been built by a superior pre-historic race, and that their degenerate descendants, known as Dero, live their still, using the fantastic machines abandoned by the ancient races to torment those of us living on the surface. One characteristic of this torment was "voices" that came from no explainable source. Thousands of readers wrote to affirm that they, too, had heard the fiendish voices from inside the earth.
Edgar Rice Burroughs, more concerned with entertainment than plausibility, also wrote tales of adventure in the inner world of Pellucidar (including, at one point, a visit from his character Tarzan). Burroughs's Pellucidar is notable for the fact that, although the inner surface of the Earth is of absolutely smaller area than the outer, those areas which are oceans on the outer surface are continents on the inner and vice-versa, so that Pellucidar actually has a greater land area than the "outer" continents combined. It is also inhabited by primitive humans and by an exciting mix of all those large and dangerous creatures which have unfortunately become extinct on the outer surface, and to which Burroughs did not hesitate to add such improvements as the Mahars, creatures vaguely resembling large intelligent pterodactyls with dangerous psychic powers. Pellucidar is lit by a central miniature sun which never sets, so that the human inhabitants have never developed the notion of time.
In the science-fiction novel Hard To Be God, written by the Russian authors Boris and Arkady Strugatsky, an Earthling space traveler lands on a planet where, due to an atmospheric peculiarity, the native population is convinced that it resides inside a concave hollow earth. As a result, they cannot accept his interplanetary origin.