In this paper we examine directed path models of polymers adsorbing at a linear boundarywhile subject to long ranged, short ranged, and periodic attractions. The generatingfunctions of these models are infinite continued fractions, which may be analyzed toexamine the free energies and bound the critical curves in the models. In each model thepath interacts with the boundary through a force that is distance dependent, and viavertices binding to the boundary with a binding energy. We recover as specialcases results for (1) the adsorption of a directed path into a thickened boundarylayer, (2) the adsorption of paths adsorbing in a periodic force field and in anenvironment with an infinite set of defect planes, (3) the adsorption of a pathsubject to a short ranged force, and finally, (4) the adsorption of a path subject toa long ranged force. In each of these models we give estimates or exact valuesof free energies and critical points. The phase diagrams of the models are alsoexamined.