A brief overview of the most recent results relevant to the impedance wedge canonical problem has been presented in this paper. It is worth noting that there are still open problems to be faced with, as well as a continuous interest in the above canonical problems due to the need of efficient high frequency techniques in effective engineering numerical codes. The authors are presently working on revisiting some known exact solutions for both isotropic and anisotropic impedance wedges on the basis of the results recently obtained by Prof. Tiberio. Work is also in progress to derive heuristic approximate diffraction coefficients for edges in penetrable screens, starting from the exact solution for the scattering at the edge of a semi-infinite planar strip grating