The contravariant power-set functor on Set is not very mysterious. The covariant power-set functor seems harder to characterise. This talk will give such a characterisation, which immediately implies its monad structure. We then explain how the same universal property comes very close to characterising the Vietoris monad on the category of compact Hausdorff spaces. With a bit more work, we can completely characterise it, and once again, reconstruct its monad structure.