Macroscopic electrodynamics described by Maxwell’s equations in matter, appropriate constitutive relations and boundary conditions may appear concluded from a physicist’s viewpoint, whose sole interest lies in the determination of electric field and magnetic flux irrespective of mechanical influences. The necessity to properly account for mutual coupling in the field of continuum electromagnetism, however, has sparked a yet undecided dispute among researchers regarding the correct formulation of electromagnetic force and torque on polarizable bodies entering the linear and angular momentum balances of continuum mechanics. Already over 100 years ago, several prominent models for the so-called Maxwell stress tensor have been proposed [1,2], which, in electrostatic considerations, dictates the acting forces and couples. As turns out, simply generalizing Coulomb’s law, whose microscopic formulation for point charges is unchallenged consensus, to include macroscopic bound charges is an assumption that must be subjected to experimental scrutiny on its own [3]. This work gives an overview of the most predominant Maxwell stress formulations for polarizable matter in conjunction with their corresponding physical interpretations. What is more, careful transformation of the integral formulations for electrostatic force and couple to their localized counterparts reveals hitherto unnoticed manifestations as concentrated loads, which strongly depend on singularities of the Maxwell stress tensor. These singularities arise naturally, among other things, in the context of electromechanical crack problems, where electric field and polarization suffer square root singularities at the tip of a semi- or impermeable crack. While investigations of dielectric fracture in most cases have been restricted to accounting for electrostatic tractions at crack faces, in this work the full effect of Maxwell stress induced loads, covering also body and concentrated line forces, is analyzed at the example of a Griffith crack. In doing so, fundamentally different contributions to crack tip loading and even higher-order stress singularities become apparent.