The development of soft materials for various smart applications, such as in soft robotic devices derived from elastomers, naturally occurring rubbers and polymers, can be traced back to 1940s. Contrary to conventional robotics, soft robotic research was primarily dedicated to reproducing and mimicking the elasticity and compliance of biological substrates. In the last few decades, however, subsequent progress in soft robotic devices and manipulators has been witnessed within the subcategories of material & processing, sensor and actuators. In this chapter, a comprehensive introduction to soft robotics engineering is highlighted exclusively from the perspective of materials development. Soft material prototypes are eventually exploited towards designing biomimetic prosthetic devices with sensing capabilities and soft actuating bodies. We present an elaborate discussion on soft materials engineering, including elastomers, polymer composites containing fillers and associated processing methodologies. Despite high flexibility and inherent biocompatibility, conventional soft elastomer-based (silicone and polyurethane) matrices often suffer from either poor mechanical strength or reduced mechanical output at higher temperatures. This review briefly summarizes and critically discusses the different types of compliant maten als, Le. elastomers, fluids, gels and others, which are currently being employed in soft robotics. This chapter also highlights new opportunities and paves some potential avenues to address several challenges, particularly the ones concerning and soft robotic materials. Moreover, utilization of soft rubber for sensors and other applications could ameliorate the versatility of soff material applications. Therefore, challenges and future direction in soft robotics research have to be explicitly integrated within the subdomain of materials development and processing and, therefore, addressed in-depth in this chapter, with an emphasis on autonomous soft robotic arms capable of stimuli-responsive operations.