For the past 130 years or so, piano manufacturers have, in general, been making pianos to pretty much the same design. The two main types of design or construction you will encounter, are straight-strung over-dampers and over-strung under-dampers. What this refers to is the configuration of the strings on the frame and the type of action fitted in the piano. As mentioned previously, these are the two most common configurations, but both straight-strung under-dampers and over-strung over-dampers are out there too, the latter being more common in pianos of German manufacture.
Below is an example of a 1920's British straight-strung over-damper piano.
Types of piano actions
Here you can see the strings of the piano running vertically from top to bottom
When you press a key on the piano, strings are struck by the hammer making the string resonate. When you then release the key, the strings are stopped from sounding (or "damped") by the dampers. The