Toward the practical applications, on operation of conduction-cooled HTS SMES at temperatures well below 77 K should be investigated, in order to take advantage of a greater critical current density of HTS and considerably reduce the size and weight of the system. Recently, research and development concerning application of the conduction-cooled HTS SMES that is easily movement are actively progressing in Korea. Electrical insulation under cryogenic temperature is a key and an important element in the application of this apparatus. However, the behaviors of insulators for cryogenic conditions in air or vacuum are virtually unknown. Therefore, this work focuses on the breakdown and flashover phenomenology of dielectrics exposed in vacuum for temperatures ranging from room temperature to cryogenic temperature. Firstly, we summary the insulation factors of the magnet for HTS SMES. And a surface flashover as well as volume breakdown in air and vacuum has been investigated with two kind insulators. Finally, we will discuss applications for the HTS SMES including aging studies on model coils exposed in vacuum at cryogenic temperature.