There are actually 4 main hollow earth theories:

The Concentric Spheres Hollow Earth Model
Edmund Halley(English astronomer - Halley's comet) in 1692, came up with this theory while trying to understand the Earth's magnetic field. In order to explain the complex movements of the field, Halley concluded that there must be at least 4 concentric shells each with their own magnetic properties.

The Polar Holes Hollow Earth Model
This theory states that at the North and south pole, there are openings between 2000 and 4000 kilometres across that open to the interior of the planet.In this theory the centre of the planet harbours a central sun that provides light and heat to the world within.

The Inverted Earth Hollow Earth Model
Cyrus Reed Teed, an herbalist and self-proclaimed alchemist, had a vision of a woman in 1869, who told him that we are living on the inside of the hollow Earth. For nearly forty years, Teed promoted his idea in pamphlets and speeches. He even founded a cult called the Koreshans (Koresh is the Hebrew equivalent of Cyrus).
It works on the principle that we are actually living inside a hollow planet right now and the centre of the planet is a point infinitely far away. All the other planets, the moon, satellites and the sun revolve around this central point.

The Complete Shell Hollow Earth Model
Based on a combination of the hollow Earth and expanding Earth theories, it provides an alternate explanation for the drifting continents phenomenon making the Plate tectonics theory obsolete.
This theory shows how the accumulation of matter during the planet forming process naturally produces a planet structured differently to what is currently theorised. It is also shown how a planet hollows out and expands under its own gravitational power.

I also note that an expedition from the US is due to search for a way in to the inner earth next year.