The paper describes and explains the most surprising Wood's anomaly: the total absorption of a plane wave by a shallow metallic grating. After a numerical and experimental evidence of the total absorption, we develop a quantitative phenomenological theory. Assuming that the anomalies are caused by the excitation of surface plasmon polaritons on the grating surface, we use theorems on analytic functions of the complex variable for representing the amplitudes of the scattered waves accurately through a phenomenological formula. The original rigorous grating theory used for numerical computations is outlined and some practical applications of strong absorptions are presented.