Cluster varieties, which arise in nature as moduli spaces of 4d theories, were given an algebraic reformulation by Gross-Hacking-Keel as log Calabi-Yau varieties obtained by non-toric blowups inside the boundary divisor of a toric variety. We propose a mirror symplectic reinterpretation of cluster varieties in terms of Weinstein handle attachments to the cotangent bundle of a torus and explain how various features of cluster theory behave under mirror symmetry. In particular, combining this symplectic presentation with microlocal-sheaf approaches to the Fukaya category should lead to a proof of homological mirror symmetry, offering a new approach to the duality conjectures of Fock-Goncharov which relate functions on a cluster variety to the tropicalization of a Langlands-dual cluster variety. (This is based on work in progress with Ian Le)