This paper characterizes the family of truthful doublesided auctions. Despite the importance of double-sided auctions to market design, to date no characterization of truthful double-sided auctions was made. This paper characterizes truthful mechanisms for double-sided auctions by generalizing Roberts classic result [29], to show that truthful double-sided auctions must ”almost” be affine maximizers. Our main result of characterizing double-sided auctions required the creation of a new set of tools, reductions that preserve economic properties. This paper utilizes two such reductions; a truth-preserving reduction and a non-affine preserving reduction. The truthpreserving reduction is used to reduce the double-sided auction to a special case of a combinatorial auction to make use of the impossibility result proved in [20]. Intuitively, our proof shows that truthful double-sided auctions are as hard to design as truthful combinatorial auctions. Two important concepts are developed i...