There are 3 species of predatory fly parasites mixed in your order: Spalangia cameroni, Muscidifurax zaraptor and Muscidifurax raptorellus.
Fly parasites search fly-breeding areas for fly pupae containing developing flies. Once inside, the eggs hatch inside the fly pupa and feed on the developing fly and after two to three weeks of feeding, an adult fly parasite emerges to repeat the cycle. Each female fly parasite can kill approximately 100 immature flies in her lifetime.
The praying mantis is an ambush hunter: it sits very still, blending in with its surroundings and waiting patiently for an unwary insect to come near. Then it easily snatches its unsuspecting victim -- some much larger than itself. When it spots one, it takes the mantis only 50-70 milliseconds to strike out with its forelegs and snare its prey. The diet of the praying mantis includes all sorts of insects and spiders, and sometimes even frogs, lizards, or mice.
Amblyseius swirskii is a very effective generalist predatory mite used to suppress immature thrips, two-spotted spider mites, cyclamen mites, broad mites, and whiteflies in ornamental, fruit and garden crops.