1. History of the Euphonium
This is a picture of Steven Mead riding an Euphonium

2. Renaissance to Baroque
The Euphonium, Similar to the Tuba came from similar ancestors. The Serpent and the Ophicleide. Both of these instruments were instrumental in the development of lower brass instruments today.

3. Renaissance to Baroque
Left: This is a picture of an Ophicleide
Right: This is a picture of a Serpent

4. Romantic to 21st Century Periods
Compensating Euphoniums: In the mid 19th century it has said to have been that a wide bore bugle with a baritone range was invented. Later in 1874 David Blaikley developed an compensating euphonium. Thus compensating euphoniums were born.
Above: Besson Euphonium

5. British Brass Band
The Euphonium, Baritone and the Eb Alto Horn are all staples of the Tuba/Euphonium family. They all play a big role in brass bands by complimenting each other while creating a very full range and timbre of middle to lower brass voices.
Right: a Baritone Horn
Below: An Euphonium
Right: an Eb
Alto Horn

6. The difference between Baritones and Euphoniums
In American bands and ensembles the instrument names, Euphoniums and Baritones, have become interchangeable, though they are two distinctly different instruments. Visually, a Baritone is usually slightly smaller in size and primarily has three valves but can have an occasional fourth. On the other hand a Euphonium is slightly larger and can have four valves upright four in front or three upright and one compensating valve accessible to the left hand. Engineering-wise they are also different. A Baritone is predominantly 2/3 cylindrical and 1/3 conical and a Euphonium is 1/3 cylindrical and 2/3 conical. This is all relative. Also This is very technical Let me explain it with some pictures.
Talk about conical and cylindrical bore
The shape to the left is a conical shape resembling the approximate shape a Euphonium is shaped in and the shape to the right is a cylindrical shape resembling the tubing for a Baritone.

7. 20th Century American Euphoniums
The Double Bell Euphonium was developed during the turn of the century. Unlike a regular Euphonium the Double Bell Euphonium consists of two bells one similar to regular Euphoniums of the time and a smaller one on the other side of the horn used for the fourth (and sometimes fifth) valves.
Commonly referred to as the “Toy” Euphonium.

8. Marching Baritones and Euphoniums
Marching Baritones/Euphoniums are used widely among many American high school and collegiate marching bands. These horns are specially adapted for the field. Instead of using bells that go up, Marching Baritones are designed similar to trumpets with the bell horizontal to the ground and having the valves work perpendicular to the tubing.
Basically an upright trumpet shaped baritone/euphonium.
Right: Marching
Euphonium
Left: Marching
Baritone