Robotic artificial muscles are a subset of artificial muscles that are capable of producing biologically inspired motions useful for robot systems, i.e., large power-to-weight ratios, inherent compliance, and large range of motions. These actuators, ranging from shape memory alloys to dielectric elastomers, are increasingly popular for biomimetic robots as they may operate without using complex linkage designs or other cumbersome mechanisms. Recent achievements in fabrication, modeling, and control methods have significantly contributed to their potential utilization in a wide range of applications. However, no survey paper has gone into depth regarding considerations pertaining to their selection, design, and usage in generating biomimetic motions. In this paper, we discuss important characteristics and considerations in the selection, design, and implementation of various prominent and unique robotic artificial muscles for biomimetic robots, and provide perspectives on next-generation muscle-powered robots.