F-2-1: Awarded to the spouse of a Korean. (Abolished--Changed to F-6 from 15 Dec 2011.)
F-2-2: A single-entry visa valid for 90 days or less issued to an underage foreign child of a Korean national.
F-2-3: Single-entry resident visa valid for one year or less issued to the spouse of a resident visa holder (F-5).
F-2-4: Recognized refugee
F-2-7: Awarded on a points-based system. It seems difficult to find details of this system on Korean government agency websites. More up-to-date information on the points system is available on various sites around the web.
F-2-99: May be awarded upon fulfilment of additional requirements after 5 years on an E-2 visa.
F-4-11: Overseas Korean
F-4-12: Descendent of Overseas Korean
F-4-13: Former D or E visa holder
F-4-14: University Graduates
F-4-15: Permanent resident of OECD country
F-4-16: Corporate Executive
F-4-17: Entrepreneur of $100,000
F-4-18: Multinational Company
F-4-19: Representative of overseas Koreans organization
F-4-20: Government Employee; Overseas Korean with a foreign nationality of a country, who is currently a member of National Assembly, or has worked for 5 years or more at government office/enterprise
F-4-21: Teacher; Overseas Korean with a foreign nationality of a country notified by the Minister of Justice of ROK, who is a university professor (including associate professor and lecturer), or a teacher at an elementary/middle/high school
F-5-11: Special Talent; recognized by the Minister of Justice for his/her excellence in a specific field including science, management, education, cultural arts, and athletics
F-6-1: Spouse of a Korean National
F-6-2: Child Raising; Father or mother of minor child born after a marriage with Korean (including de facto marriage), but not qualified for F-6-1 (spouse of Korean citizen), who is raising or is planning to raise the child in ROK