I'll discuss a package of new invariants for Legendrian knots and links that are Floer-theoretic in nature but inspired by connections to cluster varieties. The invariants include a Poisson bracket and possible q-deformation for Legendrian contact homology, as well as a symplectic structure on augmentation varieties. This talk reports on joint work in progress with Roger Casals, Honghao Gao, Linhui Shen, Daping Weng, and Eric Zaslow.