Heat-driven heat pumps based on the Vuilleumier (VM) cycle have been studied for decades due to their promising high performance for both heating and cooling. Different prototypes were built and tested, while none of them were commercialized due to construction cost. This work explains the thermodynamic principle of the VM cycle and reviews traditional VM heat pumps. A free piston VM heat pump is described as an alternative approach to reduce the construction cost. The advantages and disadvantages of free piston VM heat pumps are discussed. A thermodynamic model based on a test prototype is built for free piston VM heat pump study and analysis. The pressure and temperature variations of the heat pump are estimated by the model. The heating and cooling performance of the machine is also studied. The model results are compared to test data from the prototype heat pump. The comparison results can be used to understand the shortcomings of the current prototype and optimize the prototype design in the future.