An electrochemical and/or flow-electrode capacitive deionization module for continuous liquid desalination and/or selective separation and/or concentration and/or recombination of ions from liquids and/or energy storage and/or electrochemical reactions in liquids/electrosynthesis, comprising: an anodic compartment containing a first flow-electrode; a cathodic compartment containing a second flow-electrode; and optionally at least one liquid-permeable compartment formed between the anodic compartment and the cathodic compartment, the anodic compartment comprising a first flow passage, wherein the first flow passage is configured such that the first flow-electrode flows through said flow passage in a first flow channel embedded therein, the cathodic compartment comprising a second flow passage, wherein the second flow passage is configured such that the second flow-electrode flows through said flow passage in a second flow channel embedded therein, the first flow-electrode and the second flow-electrode each being an aqueous and/or solvent slurry containing suspended conductive particles or a mixture of conductive and non-conductive particles or particles made of a mixture of conductive and non-conductive materials, wherein the first and second flow passages are made of a non-conductive flexible material, wherein the anodic compartment and the cathodic compartment each comprise a flexible membrane-electrode assembly as current collectors, the flexible membrane-electrode assembly consists of a polymeric ion exchange membrane, and only one electrode arranged on the polymeric ion exchange membrane, and does not include any reinforcing material, wherein the polymeric ion exchange membrane is an anion-exchange membrane, a cation-exchange membrane, or a bipolar membrane, and wherein the electrode consists of a flexible sheet of woven, electrically conductive fibers, wherein the electrode of the flexible membrane-electrode assemblies faces the flow-electrodes. an anodic compartment containing a first flow-electrode; a cathodic compartment containing a second flow-electrode; and optionally at least one liquid-permeable compartment formed between the anodic compartment and the cathodic compartment, the anodic compartment comprising a first flow passage, wherein the first flow passage is configured such that the first flow-electrode flows through said flow passage in a first flow channel embedded therein, the cathodic compartment comprising a second flow passage, wherein the second flow passage is configured such that the second flow-electrode flows through said flow passage in a second flow channel embedded therein, the first flow-electrode and the second flow-electrode each being an aqueous and/or solvent slurry containing suspended conductive particles or a mixture of conductive and non-conductive particles or particles made of a mixture of conductive and non-conductive materials, wherein the first and second flow passages are made of a non-conductive flexible material, wherein the anodic compartment and the cathodic compartment each comprise a flexible membrane-electrode assembly as current collectors, the flexible membrane-electrode assembly consists of a polymeric ion exchange membrane, and only one electrode arranged on the polymeric ion exchange membrane, and does not include any reinforcing material, wherein the polymeric ion exchange membrane is an anion-exchange membrane, a cation-exchange membrane, or a bipolar membrane, and wherein the electrode consists of a flexible sheet of woven, electrically conductive fibers, wherein the electrode of the flexible membrane-electrode assemblies faces the flow-electrodes. <EOS>