Provided is an alkali metal-sulfur cell comprising: (a) a quasi-solid cathode containing about 30% to about 95% by volume of a cathode active material (a sulfur-containing material), about 5% to about 40% by volume of a first electrolyte containing an alkali salt dissolved in a solvent and an ion-conducting polymer dissolved, dispersed in or impregnated by a solvent, and about 0.01% to about 30% by volume of a conductive additive wherein the conductive additive, containing conductive filaments, forms a 3D network of electron-conducting pathways such that the quasi-solid electrode has an electrical conductivity from about 10−6 S/cm to about 300 S/cm; (b) an anode; and (c) an ion-conducting membrane or porous separator disposed between the anode and the quasi-solid cathode; wherein the quasi-solid cathode has a thickness from 200 μm to 100 cm and a cathode active material having an active material mass loading greater than 10 mg/cm2.