The SQ are a mysterious organization which acts as the main enemy in the books. It seems to act very different in the past and present however.
this page only talks about the historians. The SQ have been very different in the past. In these time periods, the SQ's are still manipulating events in it's favor to gain the political power that it has in the present. The SQ is trying to earn the control that the present day SQ already have. It is assumed that with each great break they cause, the SQ get's stronger. Getting closer to its future power. But this is also the time when the SQ are weakest. In the present they have too much power to be stopped, but in the past their Great Breaks can be prevented, and therefore causing them to lose the potential power they would have earned. This will weaken the SQ's hold on the future and make the present day SQ's weaker and less all knowing. But the SQ's are ready for this and have the Time Wardens in place to stop anyone from the future. They have been trained to notice people from the future. There are Time Wardens and the other SQ agents whose job is to try and cause Great Breaks to benifit themselves and give the SQ more power. Yet in this past, the SQ's seem to be a more secret group and, like the Hystorians, seems to only be known by its members. In the past they have confidence that the Hystorians are weak, but know that their power is at risk if any Hystorians from the future come, as it seems to be their main weakness, their power is dependent on the past.
The SQ in the present, are an all knowning group that has almost total control over the major governments of the world. Having had its hand in just about every major historical event, the SQ's have total power. It keeps its eye on everyone, and even yells at Sera's uncle when she isn't home after curfew. They are feared by many but others act as though they have a lot of respect for the SQ. They even run history museums like the Smithsonian. To be a part of the SQ's are considered a high honor, there is even some kind of reality TV show competition where the winner is declaired the next SQ's intern. The SQ's are still secretly fighting the Hystorians and trying to prevent them from getting time travel.
Recently revealed in a post on the Infinity Ring forums that the past SQ's remained secretive until World War II, after which they became bolder and stepped out of the shadows (possibly taking the credit for what they have done over the years in secret). It was also revealed that Aristotle (founder of the Hystorians) was the first casualty in the war between the 2 groups. It also seems that the Lady in Red is the current leader of the SQ in modern times. It is still unknown however what exactly SQ stands for.
The SQ and their Great Breaks are the reason why the 2012 in the first book is very different from our own. It can be assumed that once the Breaks are fixed that, 2012 will look like our own and the SQ will either be non-existant or still exist but have no power.