From the author's text: ``This is a survey article which outlines recent work on relatively continuous perturbations of analytic semigroups in Banach spaces. The results are described from the point of view of nonlinear semigroup theory. Necessary and sufficient conditions are discussed for a semilinear operator \(A+B\) to be the full infinitesimal generator of a nonlinear semigroup which provides mild solutions of the semilinear evolution quation of the form \[ (d/dt)u(t)=Au(t)+Bu(t),\quad t>0. \] Here the linear operator A is assumed to be the infinitesimal generator of an analytic semigroup in a Banach space X and the nonlinear operator B is supposed to be continuous with respect to the graph norm of a fractional power of -A.''