Replacement of the silicon dioxide thin films in metal-oxide-semiconductor structures for microelectronics with high-permittivity dielectrics (high-k) is a crucial step in the further down-scaling of microelectronic devices. Technological development of the fabrication processes and better theoretical understanding of the physical phenomena in the considered structures are demanded simultaneously. Important issues concerning high-k are discussed in this paper and directions for further development are indicated. Further progress also requires better understanding of the physical phenomena appearing in stacked high-k/interfacial layer dielectrics.