Soft surface coatings attract increasing attention due to the versatile options they provide in numerous applications e.g. in the flourishing nanomedicine and nanobiotechnology areas. Optimisation of the performance of such ion- and solvent-permeable polyelectrolytic materials requires a detailed understanding of their electrostatic properties. This task is rendered difficult by the inherent non-uniform distribution of their structural charges. In this article, we review recent advances made in the measurement and theory of the electrokinetics (electrophoresis/streaming current) of soft surface coatings that carry spatially-separated cationic and anionic charges. Examples of such charge-stratified systems are polyelectrolyte-coated particles, polyelectrolyte multilayers, particles with zwitterionic interfacial functionality, microbial cells or hard-soft composite interfaces. It is shown here that the electrokinetic features of such colloidal systems are remarkably different from those of their counterparts with homogeneously distributed cationic and anionic charges. In particular, the interplay between electrostatic and hydrodynamic flow fields developed under electrokinetic conditions in the bulk and interfacial compartments of charge-stratified colloids/films are shown to induce a reversal of their electrokinetic response (electrophoretic mobility/streaming current) that depends on the concentration of monovalent electrolyte in solution. The prerequisites for occurrence of such spectacular behaviour are theoretically identified in terms of the Debye length, the spatial length scales defining charge layering, and the typical length for flow penetration within the colloids/films. Electrophoresis and streaming current results recently reported for poly(amidoamine) carboxylated nanodendrimers, natural rubber colloids and poly(ethyleneimine)-supported lipid bilayers are further discussed to illustrate the generic electrokinetic properties of soft interfaces defined by a given stratification of their anionic and cationic structural charges.