The valve horn
Sometime between 1815 and 1820, the mechanical valve was invented. This allowed valve horn players to achieve those same "in-between" notes that handhorn players could play, but with better sound and agility. Because of tradition, players still placed their right hand inside the bell of the horn, but it wasn't required for changing notes anymore. Eventually, the valve horn was standardized as a three-valve horn in the key of F.
Around 1900, German inventors were working on a method to combine together two differently sized valve horns for a wider range and easier playing. They took the standard horn in F and merged it with the smaller horn in B flat. This new 4 valve french horn became known as the double horn and is the standard today.
More valves and other experiments
In the 20th century, inventors tried a number of different valve combinations and designs such as 5 valve horns. While these newest designs sometimes helped solve a particular problem, using a number of valve systems became too complex and there are only a few players who use something other than the standard double horn -- for example, triple horns or B flat horns with stopping valves. These players are most likely to be at the professional level of hornplaying.
A brief history of the horn — part 1