Electrically conducting hydrogels are gaining increasing attention due to their potential application in smart patches, biosensors, functional tissue engineering scaffolds, wound management, and implants. The current review focuses on these novel materials, their synthesis routes, and their composites. Special attention is paid to fabrication routes to produce functional composites with organic and inorganic components. The design of conductive hydrogels leads to inheritance of the advantages of each component and offers new features from the synergistic effects between the components, thus opening new application areas. The review also discusses the emerging role of 3D printing as an advanced approach toward new design, functionality, and material combination possibilities. The issue of lack of the spatial control with current techniques is highlighted, and possible new routes to solve it are discussed. The review will provide readers with knowledge tool to select appropriate methodology for designing desired hydrogel material composites.