  We study the leading effective interactions between the Standard Model fields
and a generic singlet CP-odd (pseudo)Goldstone boson. Two possible frameworks
for electroweak symmetry breaking are considered: linear and non-linear. For
the latter case, the basis of leading effective operators is determined and
compared with that for the linear expansion. Associated phenomenological
signals at colliders are explored for both scenarios, deriving new bounds and
analyzing future prospects, including LHC and High Luminosity LHC
sensitivities. Mono-$Z$, mono-$W$, $W$-photon plus missing energy and on-shell
top final states are most promising signals expected in both frameworks. In
addition, non-standard Higgs decays and mono-Higgs signatures are especially
prominent and expected to be dominant in non-linear realizations.
