Actually are multipurpose stadiums not only an US-American phenomenon. There are several mulitpurpose stadiums in Europe, too. But these have a completely different character than those in the USA. US-American multipurpose stadiums are often shared between baseball and American Ffootball teams. But as baseball is completely umpopular in Europe (I don't think there is any 10000+ baseball stadium in Europe), these sharing works different and makes things easier (at least for the constructor of the stadium). European multipurposes are often shared between soccer, athletics (and sometimes American Football).

As I mentioned earlier, the construction of those stadiums is pretty simple. Take a normal soccerfield, build a 400m track around it (maybe add an extra part on one side for the jumping) and build a bowl around it. Finished. An example stadium will look like this (I left away the bowl, so that it will remain understandable):

  /        _____________          \
 /        |       3     |          \
/     /-------------------------\   \
|    /   |------------------|    \   \
|   /    |                  |     \   \
|  |   5 |       1          |     |   |   4
\  \     |                  |     /   /
 \  \    |------------------|    /   /
  \  \------------2-------------/   /

1: soccer field
2: 400m track
3: jumping grounds
4: spectator ranks
5: other athletics

This picture was inspired by the Olympic Stadium in Berlin and should make one thing obvious: When watching a soccer game you are too far away. You may be able to inspect the tactical system of your team, but you are unable to distinguish players and observe if decision by the referees (fouls etc.) are right. But these stadiums also have their advantages: Being build for Olympic games you have a stadium for athletics, soccer and the ceremonies, which is large enough for huge crowds. But this again is also a disadvantage. A 100000+ stadium will not be full during regular operating. The Berlin Olympic Stadium, which was built for the 1936 Olympic Games, was originally build for more than 100000 attendants. During its 65 years of operating it was reduced to 75000 places. The Sydney Olympic Stadium was already built with the intent to reduce its size later. Another advantage of such a stadium is, that normally an athletics stadium would be unaffordable: Athletics stadiums tend to be very huge and are only used 1-3 times a year (The Berlin Olympic Stadium is the home of the ISTAF). So the costs can be reduced dramatically by using a stadium which is already in use.

But just like in the United States there's a tendency to build soccer-only stadiums. These are normally rectangular shaped and support the spectators and the players with a better atmosphere. Such stadium had already been very popular in Great Britain where they are also used for rugby. During the last decade which led to an explosion in the income of soccer clubs, more and more continental clubs, build their own stadiums. These stadiums tend to fall in one of two categories: first are the classical stadiums. These are just normal soccer stadiums. Nearly all soccer stadiums in Great Britain and the Westfalen Stadium in Dortmund, Germany fall into this category. The other category is a new one. These are high tech stadiums with a moveable roof and huge scoreboards. Such stadiums are for example the Arena in Amsterdam (which is used for NFL Europe football by the Amsterdam Admirals, too) or the Arena - Auf Schalke in Gelsenkirchen. Auf Schalke is maybe the most modern sports arena in the world. It has not only a moveable roof, but a moveable grass field, too. After a game the field can be moved outside stadium. It also has a huge video-cube above the field, consisting of 4 35m² screens, and big conference center.