It was founded with Paul VI's permission in 1969/70 to continue the traditional rite of Mass, but either drifted away from the Church or was driven out of the Church (depending on whom you ask). It went into formal schism in 1988. I don't know a lot of the history behind what led to the schism -- but it sounds like an unhappy set of events. Talks are underway to bring the group back, but SSPX seems to be making some "impertinent" demands on the Pope that are holding things up.
The SSPX leader at the time was Mgr. LeFebvre; he consecrated a bunch of new Bishops against the will of Rome.
That led to the schism, immediately. A small group then left the SSPX and is remaining within the Church--they are building a new seminary in Lincoln, NE., and also have one in Europe someplace.
Indeed the schismatic group has had talks w/Rome recently, but they went nowhere. Ratzinger is TRYING to get them back--but it doesn't look good.