The bulk of the scientific literature on Li-conducting solid (solvent-free) polymer electrolytes (SPEs) for applications such as Li-based batteries is focused on polyether-based materials, not least the archetypal poly(ethylene oxide) (PEO). A significant number of alternative polymer hosts have, however, been explored over the years, encompassing materials such as polycarbonates, polyesters, polynitriles, polyalcohols and polyamines. These display fundamentally different properties to those of polyethers, and might therefore be able to resolve the key issues restricting SPEs from realizing their full potential, for example in terms of ionic conductivity, chemical or electrochemical stability and temperature sensitivity. It is further interesting that many of these polymer materials complex Li-ions less strongly than PEO and facilitate ion transport through different mechanisms than polyethers, which is likely critical for true advancement in the area. In this review, >30 years of research on these 'alternative' Li-ion-conducting SPE host materials are summarized and discussed in the perspective of their potential application in electrochemical devices, with a clear focus on Li batteries. Key challenges and strategies forward and beyond the current PEO-based paradigm are highlighted.