The adsorption of polymers on smooth or atomistically flat substrates has been a topic of study for decades, and such systems are well-characterized. However, there is little knowledge of the complex interfaces created by adsorption on heterogeneous surfaces: these are fundamental to numerous scientific and industrial systems, including organic optoelectronics, polymer–matrix composites, protein attachment, biomimetics, lubrication, and catalysis. Focusing on physical inhomogeneities, this paper presents an overview of the field of polymer adsorption on rough surfaces, and seeks to elucidate some of the relevant molecular mechanisms. Monte Carlo simulations are employed to study freely rotating chains adjacent to self-affine substrates, exploring the influence of surface fractal dimension and amplitude. The adsorbed polymers are characterized by density profiles and chain topologies evaluated parallel and perpendicular to the nominal surface. Our results reveal chain attachment and film structure can be controlled solely by manipulating entropic factors such as surface physical heterogeneities and adsorbate molecular weight distributions.