In the past two decades, there have been huge developments in the understanding of damping in multilayered thin films and, more generally, in spin-transport in spintronic systems. In multilayered ferromagnetic (FM)/non-magnetic (NM) thin-film systems, observations of ferromagnetic resonant precession show a strong increase in the fundamental damping when the FM thin films are layered with heavy metals, such as Pt. These observations led to significant theoretical developments, dominated by the “spin-pumping” formalism, which describes the enhancement of damping in terms of the propagation or “pumping” of spin-current across the interface from the precessing magnetization into the heavy metal. This paper presents a perspective that introduces the key early experimental damping results in FM/NM systems and outlines the theoretical models developed to explain the enhanced damping observed in these systems. This is followed by a wider discussion of a range of experimental results in the context of the theoretical models, highlighting agreement between the theory and experiment, and more recent observations that have required further theoretical consideration, in particular, with respect to the role of the interfaces and proximity-induced magnetism in the heavy metal layer. The Perspective concludes with an outline discussion of spin-pumping in the broader context of spin-transport.