Magnetic phenomena are generally associated with iron and steel. In reality, magnetism is an electric phenomenon. Any moving charge is a magnet. "Ferromagnetism" is one of 3  forms of magnets atoms can take- the other two being diamagnetism and paramagnetism. Atoms are magnetic because their electrons ( and nuclei ) are moving ( spinning ) charges. Iron simply has a strong total magnetic effect when all the electrons' individual effects are added.
 

• Magnetism became associated with currents when Oersted noticed a compass move near a wire with a current in the very early 19th century.

• Faraday showed through induction the intimacy of current and magnetism.

• Maxwell combined these theoretically to explain light and radio waves.

• Einstein in his 1905 paper showed how "Special Relativity" made magnetism merely a complexion of electricity under motion. He showed that the assumption of a constant speed of light for all observers allowed all magnetic effects to be able to be derived from electrostatics!  Web page on this. ( Most text books on Special Relativity state "categorically" that Special Rel effects can only be observed at super high speeds - rubbish. Charges moving in a wire only drift along at best at centimetres each second ( mms^-1 more likely) yet magnetic effects are then easily seen!
• (PS - "E=mc²" is a side product of this theory.)

However, as Spec Rel is not easy to apply to electrostatics, we start by observing that two parallel "current carrying wires" attract when the currents have the same direction yet repel when when antiparallel.

F = 2x10^-7 I₁I₂l / r

We could start with other current type magnets attracting or repelling. The key issue is that currents attract and repel - the motor principle.

What is startling is that while the forces are measured in newtons (N) same as always, magnetism is not strictly newtonian as we shall see when we analyse the direction of the forces once we look at the fields.

The equation above is the base level reason why electric motors work, wires attracting and repelling wires.