Flexible polymer-based actuators, often also called artificial muscles, are an essential part of biomimetic systems that mimic the movement principles of animal world creatures. The most used electrode material to force the actuator move is an ensemble of noble metal nanoparticles in the electroactive polymer surface. Noble metal electrodes have enough electrical conductivity and elasticity and are not subjected to oxidation. However, high cost of such electrodes and their tendency to cracking dictate the need for searching other materials, primarily carbon ones. The review considers several options for this search. For example, carbon nanotubes and graphene have excellent properties at the level of a single individually taken nanotube or graphene sheet. However, conservation of these properties in structurally imperfect film electrodes requires a separate study. In addition, there are problems of compatibility of such electrodes with the polymers that requires cumbersome technologies, e.g., hot pressing, which complicates the production of the actuator as a whole. The review concerns the technology options of manufacturing actuators and the results obtained on their basis, both including hot pressing and avoiding this procedure. In particular, the required level of the graphene oxide reduction in hydrazine provides sufficient adhesion at rather high electrical conductivity of the graphene film. The ability to simultaneous achieving these properties is a nontrivial result, providing the same level of actuation as with expensive noble metal electrodes. Actuators that additionally require greater lifetime resource should be obtained in other ways. Among them are using the graphdiyne electrodes and laser processing of the graphene electrodes.