  Crack-like objects that propagate along frictional interfaces,
i.e.~frictional shear cracks, play a major role in a broad range of frictional
phenomena. Such frictional cracks are commonly assumed to feature the universal
square root near-edge singularity of ideal shear cracks, as predicted by Linear
Elastic Fracture Mechanics. Here we show that this is not the generic case due
to the intrinsic dependence of the frictional strength on the slip rate, even
if the bodies forming the frictional interface are identical and predominantly
linear elastic. Instead, frictional shear cracks feature unconventional
singularities characterized by a singularity order $\xi$ that differs from the
conventional $-\tfrac{1}{2}$ one. It is shown that $\xi$ depends on the
friction law, on the propagation speed and on the symmetry mode of loading. We
discuss the general structure of a theory of unconventional singularities,
along with their implications for the energy balance and dynamics of frictional
cracks. Finally, we present explicit calculations of $\xi$ and the associated
near-edge fields for linear viscous-friction -- which may emerge as a
perturbative approximation of nonlinear friction laws or on its own -- for both
in-plane (mode-II) and anti-plane (mode-III) shear loadings.
