Roughly speaking, the absorber is a set, which includes, after finite number of initial states, each trajectory of a transformation of space into itself. This paper deals with the exact definition of absorbers for linear operators, the study of the properties, the applications to “classical” dynamics and to solvability of operator equations. It is expected that the description of the structure of absorbers will add new insights to the recent discussion of nature and content of notion of attractiveness for nonlinear dynamics.