After decades of development in Li-ion batteries, solid polymer electrolytes (SPEs) are currently experiencing a renaissance as a promising category of materials to be used in all-solid-state batteries. However, a fundamental understanding of their electrochemical properties in the battery environment is still lacking, which in turn limits the implementation of this prospective solution. With the aim of bridging this knowledge gap, we have assessed, through first-principles thermodynamics calculations based on atomic-scale modeling, the electrochemistry of a range of relevant polymer electrolyte hosts in their pristine form and also when doped with commonly used Li-ion salts. A significant change of the electrochemical stability window upon formation of the polymer/salt complexes was found. The mechanisms of the reduction and oxidation reactions are unveiled and correlated to the electronic structures and molecular structural relaxations. In the reduction process, the salt anions control the potentials due to bond cleavage that stabilize the reduced state. In the oxidation process, the mechanism is different with the charge being stabilized either on the polymer or on the salt anion depending on the complex formed. This assessment of the electrochemical stability of the polymer/salt complexes could serve as a guide for electrolyte design in SPE-based all-solid-state batteries.