Trichoplax, a member of the phylum Placozoa, is a tiny ciliated marine animal that glides on surfaces feeding on algae and cyanobacteria. It stands out from other animals in that it lacks an internal digestive system and, instead, digests food trapped under its lower surface. Here we review recent work on the phenotypes of its six cell types and their roles in digestion and feeding behavior. Phylogenomic analyses place Placozoa as sister to Eumetazoa, the clade that includes Cnidaria and Bilateria. Comparing the phenotypes of cells in Trichoplax to those of cells in the digestive epithelia of Eumetazoa allows us to make inferences about the cell types and mode of feeding of their ancestors. From our increasingly mechanistic understanding of feeding in Trichoplax, we get a glimpse into how primitive animals may have hunted and consumed food prior to the evolution of neurons, muscles, and internal digestive systems.