[en] A recently developed method for calculating the widths of atomic and molecular resonances is reviewed. The method is based on the golden-rule definition of the resonance width, GAMMA(E). The method uses only square-integrable, L², basis functions to describe both the resonant and the non-resonant parts of the scattering wave function. It employs Stieltjes-moment-theory techniques to extract a continuous approximation for the width discrete representation of the background continuum. Its implementation requires only existing atomic and molecular structure codes. Many-electron effects, such as correlation and polarization, are easily incorporated into the calculation of the width via configuration interaction techniques. Once the width, GAMMA(E), has been determined, the energy shift can be computed by a straightforward evaluation of the required principal-value integral. The main disadvantage of the method is that it provides only the total width of a resonance which decays into more than one channel in a multichannel problem. A review of the various aspects of the theory is given first, and then representative results that have been obtained with this method for several atomic and molecular resonances are discussed. 28 references, 3 figures, 4 tables