This review focuses on capillary electrophoretic separations performed on capillary electrophoresis chips (CE chips) with hydrodynamically closed separation systems in a context with transport processes (electroosmotic flow (EOF)) and hydrodynamic flow (HDF)) that may accompany the separations in these devices. It also reflects some relevant works dealing with conventional CE operating under such hydrodynamic conditions. The use of zone electrophoresis (ZE), isotachophoresis (ITP) and their on-line combination (ITP-ZE) on the single-column and column-coupling CE chips with the closed separation systems and related problems are key topics of the review. Some attention is paid to sample pretreatment in the separations performed on the CE chips. Here, mainly potentialities of the ITP-ZE combination in trace analysis applications of the miniaturized systems are discussed in a broader extent. Links between the ZE separation and detection provide a frame for the discussion of current status of the detection on the CE chips. Analytical applications illustrate potentialities of the CE chips operating with the closed separation systems (suppressed HDF and EOF) to the determination of small ions present in various matrices by ZE, ITP and ITP-ZE.