Electromagnetic waves are disturbances in the electromagnetic field that do not require a medium for propagation, differing from traditional wave concepts. They are governed by Maxwell's equations, which provide solutions in a vacuum, indicating that electric and magnetic fields can exist independently of charges. The relationship between changing electric and magnetic fields leads to the formation of waves, with these fields being perpendicular to each other and to the direction of wave propagation. While the electromagnetic field itself can be viewed as the medium, this analogy may cause confusion regarding the nature of wave displacement. Understanding these concepts often requires a background in calculus and differential equations to grasp the underlying mathematics.