Because of safety concerns associated with the use of liquid electrolytes and electrolyte solutions, options for non-liquid materials like gels and polymers to be used as ion-conducting electrolytes have been explored intensely, and they attract steadily growing interest from researchers. The low ionic conductivity of most hard and soft solid materials was initially too low for practical applications in supercapacitors, which require low internal resistance of a device and, consequently, highly conducting materials. Even if an additional separator may not be needed when the solid electrolyte already ensures reliable separation of the electrodes, the electrolytes prepared as films or membranes as thin as practically acceptable, resistance may still be too high even today. Recent developments with gel electrolytes sometimes approach or even surpass liquid electrolyte solutions, in terms of effective conductance. This includes materials based on biopolymers, renewable raw materials, materials with biodegradability, and better environmental compatibility. In addition, numerous approaches to improving the electrolyte/electrode interaction have yielded improvements in effective internal device resistance. Reported studies are reviewed, material combinations are sorted out, and trends are identified.