Elastomeric materials have great application potential in actuator design and soft robot development. The most common elastomers used for these purposes are polyurethanes, silicones, and acrylic elastomers due to their outstanding physical, mechanical, and electrical properties. Currently, these types of polymers are produced by traditional synthetic methods, which may be harmful to the environment and hazardous to human health. The development of new synthetic routes using green chemistry principles is an important step to reduce the ecological footprint and create more sustainable biocompatible materials. Another promising trend is the synthesis of other types of elastomers from renewable bioresources, such as terpenes, lignin, chitin, various bio-oils, etc. The aim of this review is to address existing approaches to the synthesis of elastomers using “green” chemistry methods, compare the properties of sustainable elastomers with the properties of materials produced by traditional methods, and analyze the feasibility of said sustainable elastomers for the development of actuators. Finally, the advantages and challenges of existing “green” methods of elastomer synthesis will be summarized, along with an estimation of future development prospects.