That's the simple version. It gets incredibly complex. You see, the Conspiracy has actually been carrying out 'alien' abductions - taking people away to test their ability to carry alien genetic material (for example, babies), as part of a plan to convert humans into an alien slave race using an infection spread through bees.

It has also been working on a project, 'Purity Control', to breed human/alien hybrids, resistant to the Black Oil.

Over time, the Conspiracy has split into various factions, as it became increasingly apparent that the aliens they're working with aren't completely trustworthy. Because of this, the Conspiracy has been secretly working with groups of rebel alien clones, as well as an alien shapeshifter sent to hunt down the rebel clones, and also on developing a vaccine for the Black Oil. Certain factions of the conspiracy have even been promoting Mulder's efforts to uncover the truth, whilst other factions in the Conspiracy have been carefully misleading Mulder.