Recent experiments have shown that intense magnetic dipole radiation can be generated with light at intensities as low as 107 W/cm2 in transparent dielectrics. This surprising phenomenon has been shown to take place via a magneto-electric interaction that was overlooked in the early days of nonlinear optics and overcomes the apparent limitations on magnetic dipole (MD) effects imposed by the multipole expansion of classical electrodynamics. The phenomenon is essentially relativistic in origin but appears at sub-relativistic intensities because of parametric enhancement. Classical analysis, numerical simulations, perturbation theory, and quantum theory have been offered to analyze and explain this phenomenon. These treatments describe an oscillatory, transverse magnetic response that is driven by the product of the electric and magnetic field components of a linearly-polarized light field. The fields act jointly (despite their orthogonality) to drive a coherent dipolar magnetization in bound electron systems. Strong coupling of energy from electric to magnetic motions accounts for the appearance of large magnetic dipole (MD) moments despite the weakness of optical Lorentz forces at intensities far below the relativistic threshold (I<<1018 W/cm2).