Missiles
A Missile is a small self-propelled projectile that contains an explosive warhead and/or a sensor. Missile warheads explode on impact, creating a triangular damage pattern in armor. Missiles can also be used in a variety of other creative ways, to act as "Mines", "Drones", "Buoys", or the like.
Missiles must be designed in the Ctrl-F10 Missile Design Window, researched, built by ordnance factories on a planet, loaded onto ships' missile magazines and launched by missile launchers. They use Missile Fire Controls of the firing ship for target acquisition. Having their own sensors allows them to acquire targets on their own.
Missiles require missile launchers of an appropriate size to launch them, however missile launchers can launch smaller missiles than they were designed to accommodate, i.e. a size 5 missile launcher can launch size 1-5 missiles. Each launcher can store one mounted missile. All reloads have to be carried in missile magazines. Missiles cannot be transported in Cargo Holds. Having dedicated ammo transports (colliers) can be quite useful, both in battle and to supply outposts with missiles and mines.
Warning: there is a glitch in the game that can prevent incoming missiles from being detected and fired upon by your automated defenses if you choose a long increment time in battle. It's safer to stick to increments of under a minute.
See the Anti-Missile Tutorial for an introduction to defending against missiles.
Missile Design Basics
A simple missile will have fuel, an engine, and a warhead. This can be fired at a target, and if it hits the target, it will explode and deal damage. Missiles may also have sensors, which allow them to find their own targets, rather than needing fire control data from the launching ship.
As a general rule, combat missiles are fast. Speed is usually their best defense against point defense, and missile engines can have extraordinarily high power ratios to allow them to reach very high speeds. Warhead sizes should usually be a square number(1, 4, 9, etc.), as this maximizes penetration of armour, given the damage profile of missiles. Fuel should be sufficient for desired combat ranges, but no more, as the added weight of fuel can slow the missile down significantly.
However, other kinds of missiles exist. You can load them with geological sensors for survey work on distant bodies that aren't worth visiting with your main survey ships. Instead of an exploding warhead, you can use another whole missile as a "warhead", to create multi-stage missiles. Depending on version, there are also other options for missile enhancements (standoff laser warheads, retargeting capability, ECCM, decoys, etc.). See the version-specific pages for details.