The Venus flytrap (Dionaea) can capture insects by perceiving more than one consecutive touches, with closure motion occurring within a fraction of a second, a speed that is among the fastest in the plant kingdom. The fast motion of plants such as Dionaea, Aldrovanda (waterwheel plants) and Utricularia (bladderworts) represent fascinating examples in nature where physics, biochemistry, and engineering principles work together to fulfill biological functions. A more comprehensive understanding of these carnivorous behaviors in plants can be achieved with the joint efforts by researchers from biology, physics, chemistry, mathematics and engineering. Moreover, the principles learnt from these natural systems can be employed to develop bio-inspired structures and devices with a variety of engineering applications.