Given the scope of the human immunodeficiency virus (HIV) pandemic, millions of people will be in need of chronic antiretroviral therapy (ART) for decades into the future. It is hoped that progress in prevention of HIV infection can be made, but there have been few successes in this effort thus far. At the same time, lifelong ART presents formidable problems. Therefore, while research must continue on improvements in prevention and treatment, future HIV research should now also seek to develop temporally contained therapies capable of eradicating HIV infection. This review will explore what is known about the mechanisms that restrain HIV expression and result in persistent, latent proviral infection, and what these mechanisms tell us about potential approaches towards eradication of HIV infection.