There are a few ways to model/represent the dependence between two random variables. For example there is the linear correlation or one can write one random variable as a function of the other. Then there is also copula functions that can be used to model dependence between two variables.

I was wondering if there is another way to model/represent the dependence between two random variables other than the three I've mentioned above? Is there another way to make two random variables mathematically dependent?

I've been thinking about this for quite a while now so help is much appreciated.