This is an open-label (all people know the identity of the intervention), multicenter (more than one hospital or clinical site work on a study), roll-over study to provide continued access to RPV for human immunodeficiency virus type 1 (HIV-1) infected participants. All enrolled participants will continue to receive RPV in combination with an investigator-selected background regimen consisting of other antiretrovirals (ARVs). Participants will continue to receive RPV in this study until one of the following criteria is met (whichever comes first) as determined in the study protocol: they meet at least one of the withdrawal criteria, or the participant has been treated in this roll-over study for 4 years (48 months) or older than 12 years of age and can continue RPV treatment outside of this roll-over study by switching to locally available RPV (if commercially available and reimbursed, or accessible through another source \[example: access program or government program\]) or other locally available RPV-based regimens.