Summary: We give a geometric interpretation of cluster varieties in terms of blowups of toric varieties. This enables us to provide, among other results, an elementary geometric proof of the Laurent phenomenon for cluster algebras (of geometric type), extend D. Speyer’s example [“An infinitely generated upper cluster algebra”, Preprint, arXiv:1305.6867] of an upper cluster algebra which is not finitely generated, and show that the Fock-Goncharov dual basis conjecture is usually false.