Local (LF )and branch features (BF) of the slow-roll inflaton potential produce different effects on the spectrum and bispectrum of the primordial curvature perturbations, and they could explain some of the observed CMB anomalies. After a brief review of the theoretically predicted difference of the effects produced by LF and BF some preliminary results of the comparison with observational data are presented. The adopted approach to model the features is phenomenological but some fundamental physics models which could cause the slow-roll inflationary potential modifications are also discussed.