Abstract: We say that the manifolds X and Y form an exotic pair if the continuous functions are the same on them, but the differentiable functions are different. It was a surprising discovery of J. Milnor in 1956 that such pairs do exist. Indeed, in dimension 4 there are many such examples; their existence follows from work of M. Freedman (on the continuous side) and S. Donaldson (on the differentiable side). In the lecture we will study a particular pair of 4-dimensional X and Y and sketch the argument showing that they form an exotic pair. If time permits, we will also review the current state of art regarding exotic manifolds in dimension 4.