Nowadays, the name 'Zetas' is often used as a synonym of 'Greys,' which is not really accurate. Strictly speaking, the Zetas are the inhabitants of the solar systems of the two Zeta stars of the Reticulum Rhomboidalis constellation, which is just one of many solar systems where Greys can be found. The Zetas are a humanoid extra-terrestrial civilization, responsible for a lot of the abductions. They are "a race with many subgroups who are conducting the primary genetic experiments and abductions on present day Earth humans. Their average height is 3.5 to 4 feet. They have large craniums and extremely large eyes. Their sex is indistinguishable." (PoL)
When it comes to their intentions here on Earth, two groups can be distinguished. Overall the intent of the majority of the Zetas is benign, despite the trauma that many individuals experience in their presence. There is, however, also a minority that is more interested in colonisation and conquest (the Orion / Draconian Agenda). This latter group is said to have colonies in the Betelgeuse system, and work together with Orion and Draconian Greys.
Unlike the Orion and Draconian Greys, the Zetas are a humanoid race. In fact, their ancestors looked pretty much like modern day humans do, and lived on the Apex planet in the Lyran Constellation. But a civil war, fought with nuclear weapons, resulted in the near destruction of the planet, and the excessive radiation forced the survivors to go and live underground for several generations, thus changing the tone of their skin, and the size of their eyes. (See: Apex). Another side effect of the increased radiation was a decrease in fertility-levels forcing them to procreate through cloning and other artificial techniques. One of the reasons for the abductions is to increase the diversity of the DNA-stock used for these cloning purposes.