|The placozoan: Trichoplax adhaerens.|
The body has only two layers of cells and there is no nervous system, digestive system, or even a body cavity. As with sponges, placozoans are able to reform into a single individual after being split apart. They are quite mobile and move not unlike an amoeba, even able to readily change shape. The largest individuals were produced in laboratories and are only a few millimeters across, while wild individuals are significantly smaller. As I already mentioned, there are only two cell layers. The ventral layer (i.e. the bottom layer) is flagellated and also contains cells that excrete digestive enzymes onto its food, which is then absorbed into the cells. This animal is so poorly studied that scientists have only guessed at its preferred diet: "it sits atop the algae and protozoans on which it apparently feeds." The dorsal layer (i.e. the upper layer) is thin and has only a few flagella. Placozoans reproduce asexually with ease, and do so regularly when under observation. Though sexual reproduction has occurred in a laboratory setting, very little is known about the process and the offspring produced have never developed past the sixty-four cell stage.
As for how these strange animals relate to other animals, it's difficult to say. Studies have variously supported and rejected placing them as basal or "primitive" animals, as a relative of sponges, and as a sort of simplified cnidarian. This is despite several different forms of DNA analysis.
Sources are Biology of the Invertebrates, University of California Museum of Paleontology, and Science 2.0. Image is from Wikimedia Commons under a Creative Commons license.