Eddy-current phenomena, in the field of nondestructive evaluation--which is the field upon which we focus onto herein--can be termed as the generation of currents inside passive and essentially conductive structures affected by defects, within a properly adjusted low-frequency range, and the observation and interpretation of their electromagnetic effects nearby. A panorama of eddy-current scattering, with emphasis on its links to mainstream wavefield problems is proposed first. Then, general aspects of dyadic integral formulations that can be employed to model the behaviour of a bulky or of a thin crack in a stratified embedding medium are described. Two prototype problems (isotropic cylindrically circular and planarly layering) illustrate the compactness of such formulations, their ability to profit from meaningful approximations and the price paid in terms of the complexity of Green's dyads, some computational issues linked to the discrete calculations being discussed and a novel confrontation of experimental and numerical results being proposed. After, one focusses on general variational formulations, which leads us to finite-element methods (FEM) and their elaborate hybridisations with boundary-element methods (BEM). One aims at an educating review of these powerful methods of general applicability (time or frequency domain, uniform or nonuniform and linear or non- linear materials) that are much used in eddy-current modelling but in particular require careful discrete analysis as well as field-potential formulations tailored to the geometric and electromagnetic configuration under study; this aspect is illustrated from a canonical, yet already complex, flawed conducting torus. Finally, one outlines some present-day inversion issues, since the solution of the direct scattering problem takes full sense in nondestructive evaluation mainly at that level.