Acoustic wave sensors comprise: a piezoelectric layer, first and second electrodes arranged with the piezoelectric layer in a piezoelectric transducer circuit; and a polymeric sensing layer for adsorbing a gas-phase analyte, the adsorption of which analyte causes a change in resonant frequency of the piezoelectric transducer circuit, wherein the polymeric sensing layer comprises: (a) a polymer chosen from substituted or unsubstituted: polyarylenes comprising the reaction product of monomers comprising a first monomer comprising an aromatic acetylene group and a second monomer comprising a cyclopentadienone group; polyamides; polypyrazoles; or novolacs; or a cured product thereof; (b) a polymer chosen from substituted or unsubstituted: polyamic acids; or polyamic acid-polyimide copolymers; (c) a polymer formed from one or more monomers comprising a monomer comprising a polar group-substituted arylcyclobutene group, or a cured product thereof; or (d) a polymer comprising polymerized units of a monomer chosen from substituted or unsubstituted: maleimides; or norbomenes; or a cured product thereof. The acoustic wave sensors and methods of using such sensors find particular applicability in the sensing of gas-phase analytes.