We are all terribly afraid of them, but I feel that we don’t have enough actual information about horseflies.
There are about 3000 different species of horseflies almost all over the world. Only females bite, male horseflies don’t have the required saw-blade mouth parts and are bound to feed on flower nectar. Females actually need a certain amount of blood before they can lay eggs, which explains their aggressive behaviour. They usually choose hilltops and landmarks when they mate in swarms. As for their life cycle, they stay larvae for about one year and live as an adult horsefly for only a few days.
Horseflies are usually found in rather warm and humid environments.They are mainly attracted by dark moving objects and carbon di-oxide, which makes hikers wearing black gear their perfect prey.
Their main predators are birds that eat their larvae. In America however, there seems to be a species that especially hunts them: the horse guard wasp, which seems to find its purpose in keeping the horsefly population down.
As for their veterinary impact, they are indeed considered a “livestock pest”, reducing the weight gain of kettle and serving as transmitters for various animal diseases.
This website has some extensive guides about getting rid of horse flies by using traps: http://www.getridoffliesguide.com/how-to-get-rid-of-horse-flies/. An interesting but perhaps very tedious one is making use of horseflies’ attraction to dark moving objects, involving some tough string, a hanging stool and a black ball.