This talk is based on my recent work [arXiv:2406.19083, 2408.12146, 2505.05142]. The first concerns the majoron, a light (pseudo–Nambu–Goldstone) boson from the spontaneous breaking of U(1) lepton symmetry. We relate its breaking scale and soft mass by requiring the majoron to constitute dark matter. A minimal extension induces an electromagnetic anomalous coupling, yielding a parameter region overlapping with the QCD axion dark matter band—suggesting that axion searches may also probe the majoron. Motivated by the no-axion scenario, the second half of the talk focuses on axion-less solutions to the strong CP problem. One approach uses higher-dimensional compactifications, while another employs a non-invertible symmetry to construct the three-zero texture of the quark mass matrix.