Among four types of two-Higgs-doublet models with natural flavor conservation, the type X (lepton-specific) model is a unique option to explain the observed anomaly of muon g-2 as it allows for a light pseudoscalar and large tanbeta. We show how the parameter space explaining the muon g-2 deviation is (not) constrained by other (hadronic) leptonic observables, and study the LHC perspective to find a light pseudoscalar predicted in this scenario. Finally, we discuss the Higgs-portal nature of scalar singlet dark matter added to this framework.