Alternative chicane-type beam lines are proposed for exact emittance exchange between transverse phase space ðx; x 0 Þ and longitudinal phase space ðz; Þ, where x is the transverse position, x 0 is the transverse divergence, and z and are relative longitudinal position and energy deviation with respect to the reference particle. Methods to achieve exact phase space exchanges, i.e., mapping x to z, x 0 to , z to x, and to x 0 , are suggested. Schemes to mitigate and completely compensate for the thick-lens effect of the transverse cavity on emittance exchange are studied. Some applications of the phase space exchange for advanced beam manipulation and diagnostics are discussed.