Introduction of cART in 1996 has drastically increased the life expectancy of people living with HIV-1. However, this treatment has not allowed cure as cessation of cART is associated with a rapid viral rebound. The main barrier to the eradication of the virus is related to the persistence of latent HIV reservoirs. Evidence is now accumulating that purging the HIV-1 reservoir might lead to a cure or a remission. The most studied strategy is the so called "shock and kill" therapy. This strategy is based on reactivation of dormant viruses from the latently-infected reservoirs (the shock) followed by the eradication of the reservoirs (the kill). This review focuses mainly on the recent advances made in the "shock and kill" therapy. We believe that a cure or a remission will come from combinatorial approaches i.e. combination of drugs to reactivate the dormant virus from all the reservoirs including the one located in sanctuaries, and combination of strategies boosting the immune system. Alternative strategies based on cell and gene therapy or based in inducing deep latency, which are evoked in this review reinforce the idea that at least a remission is attainable.