In this article a review is given of the theory of stationary abstract kinetic equations. Starting from the method of singular eigenfunction expansion as developed  in the 1960’s and its subsequent  rigorous counterparts, a fairly complete view is given of the history of these problems. First the theory of abstract kinetic equations in plane parallel media is discussed. Existence and uniqueness issues, formulations of the boundary value problems in integral form  and representations of solutions in terms of solutions of certain one-variable non-linear integral equations will be treated in some detail. Finally a comparison is made of the relative merits of the various methods of solving stationary kinetic equations.