The quest for sources of the simultaneous violation of $C$ and $CP$ symmetry was popular in the 1960s, but has since been neglected for a long time. We revisit the operators that break $C$ and $CP$ for flavor-conserving transitions in both the Standard Model effective field theory and the low-energy effective field theory, which subsequently can be matched to light-meson physics using chiral perturbation theory. As applications, we discuss in particular the $C$-odd Dalitz plot asymmetries in $\eta\to3\pi$, but also decays with dilepton pairs in the final state, such as long-distance contributions to the rare semileptonic decays $\eta\to\pi^0\ell^+\ell^-$ as well as asymmetries in $\eta^{(\prime)} \to \gamma \ell^+\ell^-$ and $\eta^{(\prime)} \to \pi^+\pi^-\ell^+\ell^-$.