Infections by the human immunodeficiency virus type 1 (HIV-1), the causative agent of the acquired immunodeficiency syndrome (AIDS), are still totaling an appalling 36.7 millions worldwide, with 1.1 million AIDS deaths/year and a similar number of yearly new infections. All this, in spite of the discovery of HIV-1 as the AIDS etiological agent more than 30 years ago and the introduction of an effective combinatorial antiretroviral therapy (cART), able to control disease progression, more than 20 years ago. Although very effective, current cART is plagued by the emergence of drug-resistant viral variants and most of the efforts in the development of novel direct-acting antiviral agents (DAAs) against HIV-1 have been devoted toward the fighting of resistance. In this review, rather than providing a detailed listing of all the drugs and the corresponding resistance mutations, we aim, through relevant examples, at presenting to the general reader the conceptual shift in the approaches that are being taken to overcome the viral resistance hurdle. From the classic ‘running faster’ strategy, based on the development of novel DAAs active against the mutant viruses selected by the previous drugs and/or presenting to the virus a high genetic barrier toward the development of resilience, to a ‘jumping higher’ approach, which looks at the cell, rather than the virus, as a source of valuable drug targets, in order to make the cellular environment non-permissive toward the replication of both wild-type and mutated viruses.