The advent of polymer electrolytes was perfectly timed with the enormous increase in computational power and availability in the early 1980's. Thus we could/should expect a pool of knowledge to be available from all modelling efforts; MD or MC simulations, analytical approaches, FEM, ab initio/DFT, etc. This would be especially valuable when (now again) more emphasis is directed towards safer electrolytes in general and all solid-state electrolytes and batteries in particular - where polymer electrolytes has a major role to play. Here the main lines of polymer electrolyte modelling research both historical and current, as well as the balance between fundamentals/materials/applications, and especially what we might be missing to address, are brought forward. As a result the emphasis has historically clearly been on PEO and PPO based polymer electrolytes aimed at Li and Na batteries application. This mini-review is largely based on the plenary lecture delivered at the ISPE-14 conference held in Geelong, Australia during August 2014 and on the ISPE1-13 conference proceedings. (C) 2015 Elsevier Ltd. All rights reserved.