The coming decade will bring dramatic improvements in the axion dark matter program as new experimental designs move beyond the proof of principle stage. In this talk I will outline two new ideas that exploit this experimental progress. The first is to combine the results from two or more instruments in order to perform interferometry directly on the dark-matter wave. This technique reveals aspects of the axion signal that can be invisible to a single detector, such as the incident direction of the dark-matter wave. The second is to search for relativistic axions in these experiments, in particular future instruments like dark-matter radio will be sensitive to axions produced in the early universe that constitute a residual Cosmic axion Background (CaB). Existing searches at, for instance ADMX, are not yet sensitive to a cosmic relic, although if relativistic axions are produced in the late universe, by for instance dark-matter decaying to axions, then this is a signal the experiments are already sensitive to, but would miss with existing analyses.