Not as far as we'd like to be, But there might be good news instead. First there is Gardasil, a vaccine to eliminate the four most prevalent strands of HPV
Secondly most of the time wart and abnomal cells go away on there own after anywhere from 1 to 8 months. Newer studies are showing that HPV often is COMPLETELY eliminated by itself, to the point it is not even found in the DNA anymore. This often happens within two years. But there is no good test to tell if it's gone for the mass public yet. Some older studies say a long as there are no abnormal cells/ warts present the virus becomes dormant making it no longer contagious. However older studies say it is still in the body and with a major Immune system failing (such as HIV or organ transplant) that it can come back out again.
Where we are not closer to a cure the more we know about it and the more we educate people the better we can get at treating and preventing HPV. Over 80% of the sexually active population get HPV at one time or another most just don't know it and many strains aren't serious.
I wish we were closer.....