The electromagnetic force (or electromagnetism) is one of the four fundamental forces in nature. The electromagnetic force manifests itself through the forces between charges (Coulomb's law) and the magnetic force, both of which are summarised by the Lorentz force law.
Fundamentally, both magnetic and electric forces are manifestations of an exchange of photons. The quantum approach to the electromagnetic force is called quantum electrodynamics. The electromagnetic force is a force of infinite range which obeys the inverse square law (similarly to gravitational force).