In North and South Korea, Special cities, Metropolitan Cities, and Directly Governed Cities are cities that have a status equivalent to that of Provinces (Do). Hence, like the provinces, such cities are under the direct administration of the central government.
As of 2004, there are two Directly Governed Cities (Chikhalsi; 직할시; 直轄市) and three other special provincial-level administrative regions in North Korea; and one Special City (Teukbyeolsi; 특별시; 特別市) and six Metropolitan Cities (Gwangyeoksi; 광역시; 廣域市) in South Korea. Before 1995, the five largest Gwangyeoksi in South Korea were classified as Chik'alshi (i.e. Chikhalsi in McCune-Reischauer romanization; now spelled Jikhalsi in the Revised Romanization of Korean).
In the following tables, "Split time" shows when the city split from the province it was located in.

North Korea

Ch'ŏngjin City (Ch'ŏngjin-si; 청진시; 淸津市) was a Directly Governed City from 1960 to 1967 and again from 1977 to 1985, but is now part of North Hamgyŏng Province.
Hamhŭng City (Hamhŭng-si; 함흥시; 咸興市) was a Directly Governed City from 1960 to 1967, but is now part of South Hamgyŏng Province.
Kaesŏng City (Kaesŏng-si; 개성시; 開城市) (distinct from Kaesŏng Industrial Region) was a designated Region (Chigu; 지구; 地區) from 1951 to 1955 and a Directly Governed City from 1955 to 2003, but is now part of North Hwanghae Province.
Namp'o Special City (Namp'o T'ŭkkŭpsi; 남포 특급시; 南浦特級市) was a Directly Governed City from 1980 to 2004, but is now part of South P'yŏng'an Province. Sources

Notes

There is no Hanja for "Seoul," but in Chinese, it is written by its Joseon Dynasty name Hanseong (漢城). The new Chinese name, 首爾/首尔, is a transcription based on the pronunciation of "Seoul". As a suffix, the character gyeong (京) is used, which means "capital".
Seoul was designated a "Special Free City" (Teukbyeol Jayusi; 특별 자유시; 特別自由市) separate from Gyeonggi Province on August 15, 1946; it became a "Special City" on August 15, 1949.