A goodwill trip to North-Korea in 1966 caused General Choi (He was president of the Korean TKD Association at that time) to fall in disgrace in the eyes of the South-Koreans. Choi resigned as president of the K.T.A. and founded the I.T.F. on March, the 22nd of that same year. Headquarters were established in Canada.
ITF started concentrating on the forms developed by General Choi, while the KTA (became the WTF on May 28, 1973) concentrated on the Palgwe's. Later the WTF abbandoned the Palgwe's and started concentrating on TaeGuks. Slowly, the WTF emphasis turned to sparring. This is also the reason why a lot of people rather call (WTF) TaeKwonDo a sport than a Martial Art.
The American TaeKwonDo Association (ATA) is a smaller organisation, and has many similarities to the ITF. The ATA has a copyright on the forms of the organisation, so these forms cannot be used on competitions by non-members. There are many organisations, but the three mentioned above have the most members.
ITF practises the semi-contact part of TaeKwonDo, while WTF practises the full-contact part. ITF also focuses more on the traditional way. Since the break-up, there have been many attempts to reunite WTF and ITF, sofar without succes. There probably will never be a union within Taekwondo.