Some scientists posit that warp speed travel is possible, but as of 2015 the technology is still highly theoretical and would require years of extensive research and development to become a reality. Even after the technology is developed, it would need to be thoroughly tested.
Experts still don't know how warp travel would affect the human body. Some warp speed theories include the use of a "warp bubble," but that may cause damage to human tissue. Based on where technology stands now, it's likely that humans could reach warp-speed travel toward the end of 21st century at the very earliest.