The deepest hole drilled to date is the SG-3 borehole which is deep, part of the Kola Superdeep Borehole project, and thus visual knowledge of the Earth's structure extends that far.
Edmund Halley in 1692 put forth the idea of Earth consisting of a hollow shell about 500 miles (800 km) thick, two inner concentric shells and an innermost core, about the diameters of the planets Venus, Mars, and Mercury. Atmospheres separate these shells, and each shell has its own magnetic poles. The spheres rotate at different speeds. Halley proposed this scheme in order to explain anomalous compass readings. He envisaged the atmosphere inside as luminous (and possibly inhabited) and speculated that escaping gas caused the Aurora Borealis.
De Camp and Ley have claimed (in their Lands Beyond) that Leonhard Euler also proposed a hollow-Earth idea, getting rid of multiple shells and postulating an interior sun 600 miles (1000 km) across to provide light to advanced inner-Earth civilization (but they provide no references). However in his Letters to a German princess Euler describes a thought experiment involving a patently solid Earth.
De Camp and Ley also claim that Sir John Leslie expanded on Euler's idea, suggesting two central suns named Pluto and Proserpine (this was unrelated to the dwarf planet Pluto, which was discovered and named some time later). Leslie did propose a hollow Earth in his 1829 Elements of Natural Philosophy (pp. 449-453), but does not mention interior suns.
Jeremiah Reynolds also delivered lectures on the "Hollow Earth" and argued for an expedition. Reynolds went on an expedition to Antarctica himself but missed joining the Great U.S. Exploring Expedition of 1838 - 1842, even though that venture was a result of his agitation.
Though Symmes himself never wrote a book about his ideas, several authors published works discussing his ideas. McBride wrote Symmes' Theory of Concentric Spheres in 1826. It appears that Reynolds has an article that appeared as a separate booklet in 1827: Remarks of Symmes' Theory Which Appeared in the American Quarterly Review. In 1868, a professor W.F. Lyons published The Hollow Globe which put forth a Symmes-like Hollow Earth hypothesis, but didn't mention Symmes. Symmes's son Americus then published The Symmes' Theory of Concentric Spheres to set the record straight.
An early twentieth-century proponent of hollow Earth, William Reed, wrote Phantom of the Poles in 1906. He propounded the idea of a hollow Earth, but without interior shells or inner sun.
Marshall Gardner wrote A Journey to the Earth's Interior in 1913 and an expanded edition in 1920. He placed an interior sun in the hollow Earth. He even built a working model of the hollow Earth and patented it (#1096102). Gardner made no mention of Reed, but did take Symmes to task for his ideas. In the same time Vladimir Obruchev wrote a fiction novel Plutonia, where the hollow Earth's interior possessed one inner (central) sun and was inhabited by prehistoric species. The interior was connected with the surface by a hole in the Arctic.
Other writers have proposed that "ascended masters" of esoteric wisdom inhabit subterranean caverns or a hollow Earth. Antarctica, the North Pole, Tibet, Peru, and Mount Shasta in California, USA, have all had their advocates as the locations of entrances to a subterranean realm referred to as Agarttha, with some even advancing the hypothesis that UFOs have their homeland in these places.
A book allegedly by a "Dr.Raymond Bernard" which appeared in 1969, The Hollow Earth, exemplifies this idea. The book rehashes Reed and Gardner's ideas and ignores Symmes. Bernard also adds his own ideas: UFOs come from the interior, the Ring Nebula proves the existence of hollow worlds, etc. An article by Martin Gardner revealed that Dr.Walter Siegmeister used the pseudonym `Bernard', but not until the publishing of Walter Kafton-Minkel's Subterranean Worlds: 100,000 years of dragons, dwarfs, the dead, lost races & UFOs from inside the Earth, in 1989, did the full story of Bernard/Siegmeister become well known.
The pages of the science fiction pulp magazine Amazing Stories promoted one such idea from 1945 to 1949 as "the Shaver Mystery". The magazine's editor, Ray Palmer, ran a series of stories by Richard Sharpe Shaver supposedly claimed as factual, though presented in the context of fiction. Shaver claimed that a superior pre-historic race had built a honeycomb of caves in the Earth, and that their degenerate descendants, known as "Dero", live there still, using the fantastic machines abandoned by the ancient races to torment those of us living on the surface. As one characteristic of this torment, Shaver described "voices" that purportedly came from no explainable source. Thousands of readers wrote to affirm that they, too, had heard the fiendish voices from inside the Earth.
Fantastic stories (supposedly believed as factual within fringe circles) have also circulated that Adolf Hitler and some of his followers escaped to hollow lands within the Earth after World War II via an entrance in Antarctica. (See also Hitler's supposed adherence to concave hollow-Earth ideas, below.)
Some writers have proposed building megastructures that have some similarities to a hollow Earth -- see Dyson sphere, Globus Cassus.
Instead of saying that humans live on the outside surface of a hollow planet, sometimes called a "convex" hollow-Earth hypothesis, some have claimed that our universe itself lies in the interior of a hollow world, calling this a "concave" hollow-Earth hypothesis. The surface of the Earth, according to such a view, might resemble the interior shell of a Dyson sphere. Generally, scientists have taken neither type of speculation seriously.
Cyrus Teed, an eccentric doctor from upstate New York, proposed such a concave hollow Earth in 1869, calling his scheme "Cellular Cosmogony". Teed founded a cult called the Koreshan Unity based on this notion, which he called Koreshanity. The main colony survives as a preserved Florida state historic site, at Estero, but all of Teed's followers have now died. Teed's followers claimed to have experimentally verified the concavity of the Earth's curvature, through surveys of the Florida coastline making use of "rectilineator" equipment.
Several twentieth-century German writers, including Peter Bender, Johannes Lang, Karl Neupert, and Fritz Braun, published works advocating the hollow Earth hypothesis, or Hohlweltlehre. Stories have even been circulated, although apparently without historical documentation, that Hitler was influenced by concave hollow-Earth ideas and sent an expedition in an unsuccessful attempt to spy on the British fleet by aiming cameras up into the sky (Wagner, 1999).
The Egyptian mathematician Mostafa Abdelkader authored several scholarly papers working out a detailed mapping of the concave Earth model. See M. Abdelkader, "A Geocosmos: Mapping Outer Space Into a Hollow Earth," 6 Speculations in Science & Technology 81-89 (1983). Abstracts of two of Abdelkader's papers also appeared in Notices of the American Mathematical Society, (Oct. 1981 and Feb. 1982).
In one chapter of his book On the Wild Side (1992), Martin Gardner discusses the hollow Earth model articulated by Abdelkader. According to Gardner, this hypothesis posits that light rays travel in circular paths, and slow as they approach the center of the spherical star-filled cavern. No energy can reach the center of the cavern, which corresponds to no point a finite distance away from Earth in the widely accepted scientific cosmology. A drill, Gardner says, would lengthen as it traveled away from the cavern and eventually pass through the "point at infinity" corresponding to the center of the Earth in the widely accepted scientific cosmology. Supposedly no experiment can distinguish between the two cosmologies. Martin Gardner notes that "most mathematicians believe that an inside-out universe, with properly adjusted physical laws, is empirically irrefutable". Gardner rejects the concave hollow Earth hypothesis on the basis of Occam's Razor.
In a trivial sense, one can always define a coordinate transformation such that the interior of the Earth becomes "exterior" and the exterior becomes "interior". (For example, in spherical coordinates, let radius r go to R²/r where R is the Earth's radius.) Such transformations would require corresponding changes to the forms of physical laws; the consensus suggests that such theories tend towards sophistry.
The mass of the planet also indicates that the hollow Earth hypothesis is unfeasible. Should the Earth be largely hollow, its mass would be much lower and thus its gravity on the outer surface would be much lower than it currently is.