Background During the past 35 years, highly effective ART has saved the lives of millions of people worldwide by suppressing viruses to undetectable levels. However, this does not translate to the absence of viruses in the body as HIV persists in latent reservoirs. Indeed, rebounded HIV has been recently observed in the Mississippi and California infants previously thought to have been cured. Hence, much remains to be learned about HIV latency, and the search for the best strategy to eliminate the reservoir is the direction current research is taking. A systems-level approach that fully recapitulates the dynamics and complexity of HIV-1 latency In vivo and is applicable in human therapy is prudent for HIV eradication to be more feasible. Objectives The main barriers preventing the cure of HIV with antiretroviral therapy have been identified, progress has been made in the understanding of the therapeutic targets to which potentially eradicating drugs could be directed, integrative strategies have been proposed, and clinical trials with various alternatives are underway. The aim of this review is to provide an update on the main advances in HIV eradication, with particular emphasis on the obstacles and the different strategies proposed. The core challenges of each strategy are highlighted and the most promising strategy and new research avenues in HIV eradication strategies are proposed. Methods A systematic literature search of all English-language articles published between 2015 and 2019, was conducted using MEDLINE (PubMed) and Google scholar. Where available, medical subject headings (MeSH) were used as search terms and included: HIV, HIV latency, HIV reservoir, latency reactivation, and HIV cure. Additional search terms consisted of suppression, persistence, establishment, generation, and formation. A total of 250 articles were found using the above search terms. Out of these, 89 relevant articles related to HIV-1 latency establishment and eradication strategies were collected and reviewed, with no limitation of study design. Additional studies (commonly referenced and/or older and more recent articles of significance) were selected from bibliographies and references listed in the primary resources. Results In general, when exploring the literature, there are four main strategies heavily researched that provide promising strategies to the elimination of latent HIV: Haematopoietic Stem-Cell Transplantation, Shock and Kill Strategy, Gene-specific transcriptional activation using RNA-guided CRISPR-Cas9 system, and Block and Lock strategy. Most of the studies of these strategies are applicable in vitro, leaving many questions about the extent to which, or if any, these strategies are applicable to complex picture In vivo. However, the success of these strategies at least shows, in part, that HIV-1 can be cured, though some strategies are too invasive and expensive to become a standard of care for all HIV-infected patients. Conclusion Recent advances hold promise for the ultimate cure of HIV infection. A systems-level approach that fully recapitulates the dynamics and complexity of HIV-1 latency In vivo and applicable in human therapy is prudent for HIV eradication to be more feasible. Future studies aimed at achieving a prolonged HIV remission state are more likely to be successful if they focus on a combination strategy, including the block and kill, and stem cell approaches. These strategies propose a functional cure with minimal toxicity for patients. It is believed that the cure of HIV infection will be attained in the short term if a strategy based on purging the reservoirs is complemented with an aggressive HAART strategy.