The α-channeling effect entails the use of radio-frequency waves to expel and cool high-energetic α particles born in a fusion reactor; the device reactivity can then be increased even further by redirecting the extracted energy to fuel ions. Originally proposed for tokamaks, this technique has also been shown to benefit open-ended fusion devices. Here, the fundamental theory and practical aspects of α channeling in mirror machines are reviewed, including the influence of magnetic field inhomogeneity and the effect of a finite wave region on the α-channeling mechanism. For practical implementation of the α-channeling effect in mirror geometry, suitable contained weakly-damped modes are identified. In addition, the parameter space of candidate waves for implementing the α-channeling effect can be significantly extended through the introduction of a suitable minority ion species that has the catalytic effect of moderating the transfer of power from the α-channeling wave to the fuel ions.