  The couplings of axion-like particles are probed by different experiments
across a huge range of energy scales. Accordingly, a consistent analysis of the
corresponding constraints requires the use of the renormalization group
equations. We compute the full one-loop renormalization group evolution of all
-- relevant and marginal -- parameters in the effective field theory for
axion-like particles up to dimension five, above and below the electroweak
scale, assuming only that new physics does not violate CP. We also include a
detailed discussion of the different bases used in the literature, the
relations among them and the interplay of the CP and shift symmetries.
