What to look for in a running shoe

Midsole: Placed between the insole and the outsole, this layer of spongy material can vary in make-up. EVA (ethylene vinyl acetate) is still pretty much the standard.
Heel counter: The typically plastic insert at the back of the shoe is responsible for providing rearfoot support, allowing for or combatting against pronation and protecting the Achilles.
Outsole: The material can be blown runner, better for flexibility and cushioning, or more durable carbon rubber. Look at the lugs (the tread) on the very bottom of the shoe. The deeper the lug, obviously the better the grip.
Upper: What you’re looking for in the uppermost part of the shoe depends on your needs. For example, a racing shoe would try to save a few grams here, whereas a trail shoe would offer a bit more protection than a road shoe.
Tongue: It can help to provide extra support.
Last: This is the three-dimensional mould of the shoe - the 'shape'. It can be curved, semi-curved and straight. Lighter shoes will tend to be curved, whereas those providing the most support use a straight last.
Toe box: The width for your toes tends to vary from shoe to shoe. How much you need will depend on the make-up of your own foot and personal preference