Abstract.—The essence of an in-medium formulation of electromagnetism is the use of electric and magnetic multipole moment to characterize the intrinsic charge and current densities, which has wide applications in various fields of physics.  In this talk, I will show that, in the context of solid state physics, the magnetic quadrupole moment is a unifying concept that connects a wide range of magnetoelectric effects in crystals.  I will discuss the relation of quadrupole moment to the magnetoelectric coupling and nonlinear transport based on general thermodynamic principles.  I will then review some of our own recent work on the microscopic theory of magnetic quadrupole moment in crystalline solids and discuss its implications in several concrete examples, including nonlinear thermoelectric transport in metallic antiferromagnet.