A case against models of natural ultralight dilaton dark matter will be presented followed by a description of a new model of ultralight dark matter (UDM) in the context of the Nelson-Barr (NB) models. The NB-UDM is associated with the solution of the strong CP problem. It leads to unique set of signals, very different than those of the celebrated QCD axion UDM, such as the oscillation of the CKM CP phase and angles. These can be searched for in array of experiments from the B and Kaon factories to existing tabletop experiments, and especially via the much anticipated nuclear clock.
