Nematode-trapping fungi develop complex trapping devices to capture and consume nematodes. The dynamics of these organisms is especially important given the pathogenicity of nematodes and, consequently, the potential application of nematode-trapping fungi as biocontrol agents. Furthermore, both the nematodes and nematode-trapping fungi can be easily grown in laboratories, making them a unique manipulatable predator-prey system to study their coevolution. Several different aspects of these fungi have been studied, such as their genetics and the different factors triggering trap formation. In this review, we use the nematode-trapping fungus Arthrobotrys oligospora (which forms adhesive nets) as a model to describe the trapping process. We divide this process into several stages; namely attraction, recognition, trap formation, adhesion, penetration, and digestion. We summarize the latest findings in the field and current knowledge on the interactions between nematodes and nematode-trapping fungi, representing both sides of the predator-prey interaction.