In standard ΛCDM with simple single-field inflation, any local-type primordial non-Gaussianity is expected to be nearly scale independent, so the parameter f_NL should not show strong “running” with wavenumber beyond small model-dependent corrections (Komatsu & Spergel 2001; Bartolo et al. 2004). Yet both CMB and large-scale structure studies have explored, and in some cases weakly preferred, scale-dependent or running non-Gaussianity to explain features such as suppressed small-scale power or environment-dependent clustering, which are difficult to reconcile with a strictly constant f_NL in the minimal ΛCDM picture (LoVerde et al. 2008; Becker et al. 2012).