Humans throughout history have always sought to mimic the appearance, mobility, functionality, intelligent operation, and thinking process of biological creatures. This field of biologically inspired technology, having the moniker biomimetics, has evolved from making static copies of human and animals in the form of statues to the emergence of robots that operate with realistic appearance and behavior. Technology evolution led to such fields as artificial muscles, artificial intelligence, artificial vision and biomimetic capabilities in materials science, mechanics, electronics, computing science, information technology and many others. One of the newest fields is the artificial muscles, which is the moniker for electroactive polymers (EAP). Efforts are made worldwide to establish a strong infrastructure for this actuation materials ranging from analytical modeling and comprehensive understanding of their response mechanism to effective processing and characterization techniques. The field is still in its emerging state and robust materials are still not readily available however in recent years significant progress has been made. To promote faster advancement in the field, in 1999, the author posed a challenge to the research and engineering community to develop a robotic arm that would wrestle against human opponent and win. Currently, he is considering setting up the first competition in 2005. This paper covers the current state-of-the-art and challenges to making biomimetic robots using artificial muscles.