Damselflies and Dragonflies These insects belong to the order Odonata. They are predatory insects that are beautiful and beneficial, as they eat lots of mosquitos. Damselflies American Bluet American bluet damselflies are a brilliant blue color. Dragonflies Autumn Meadowhawk Autumn meadowhawks zip around our yard for much of the summer and into autumn, gobbling up mosquitos and other small bugs. Canada Darner Canada darners are large dragonflies with blue (male) or green (female) markings running down their sides.