Europe and China: long distance, close partners?

If we have a look at Europe and China, at first sight we do not observe too much the two entities have in common. First of all, they share no geographical borders -this applies equally to the EU- US relations- but second and more important we share not
the same cultural roots, the language and belief are completely different. So what is the interest, on which the cooperation is build on? Is it more than the accumulated trade interest the single European nation states have in China already for centuries? And what are the roles of the two entities in this cooperation?