Starting from Mordell, many conjectures have been put forward (and proved) about how geometry influences the behaviour of diophantine problems. It turns out that many of them can be put in a common framework about varieties that for dimensional reasons we do not expect to intersect. Whenever they do we say that this intersection is "unlikely". In this talk we will introduce the tools to state a quite broad conjecture of this type, known as Zilber-Pink Conjecture, and look at some special cases and consequences.