I was wondering if anyone has had any experience with using praying mantises for pest control, and what kinds of pests could be managed with them?
Mantids are not spectacular for pest control because they're very indiscriminate in choosing their prey. They readily attack other beneficial insects as well as harmful or pest insects.
I always get a few each year, usually around something that is blooming. In my area, they like to sit and wait for pollinators.
They like to attack larger prey and tend to stay away from the tiny insects like whiteflies or aphids. If you're looking for a good pest control solution for smaller insects like those, green lacewing larvae are an excellent choice (not ladybugs!).
If you have a cucumber beetle, Japanese beetle, squash vine borer, or squash bug problem, mantids may be beneficial for you, especially as these pests are often resistant to pesticides.
They are best utilized when purchased young as they will grow up eating small things and will eat larger things eventually as the grow. It is important to space them out when they are young as they tend to resort to cannibalism if left hungry for too long.
Some kinds of mantis will actually roam around hunting prey rather than waiting to ambush it.
Pest control uses
Organic gardeners who avoid pesticides may encourage mantises as a form of biological pest control. During fall in temperate regions, mantis females typically deposit an ootheca on the underside of a leaf or on a twig, and in some species these are harvested commercially. If the egg case survives winter, the offspring, called nymphs, emerge in late spring or early summer. The nymphs have voracious appetites and typically cannibalize each other if they cannot find an adequate supply of aphids and other small insects. Tens of thousands of mantis egg cases are sold each year in some garden stores for this purpose. However, mantises prey on neutral and beneficial insects as well, basically eating anything they can successfully capture and devour. (source)
Diet changes over lifetime
Insects form their primary prey, but the diet of a mantis changes as it grows larger. In its first instar a mantis eats small insects such as tiny flies or its own siblings. In later instars it does not or cannot profitably pursue such small prey. In the final instar as a rule the diet still includes more insects than anything else, but large species of mantis have been known to prey on small scorpions, lizards, frogs, birds, snakes, fish, and even rodents; they feed on any species small enough for them to capture, but large enough to engage their attention. For example, a large mantis feeding on a bee or bug might be pestered with impunity by jackal flies and biting midges that it would readily have eaten in its first instar. Large prey tends to increase in value with the cube of its size: a blowfly four times as long as a jackal fly represents a meal about 64 times as massive. (source)