Methods and apparatus that enable a subscriber of an adaptive bitrate streaming service provider to begin viewing a live program already in progress, and further have the ability to pause, rewind or start the program over from the beginning of the program regardless of its actual length or the manifest window defined by an encoder. Selective retrieval of a live media stream is provided by storing, at a server, a plurality of media fragments beginning at an initial time along with a server manifest for the media stream. In response to a client request for a start time later than the initial time, the server generates a program-specific manifest based on the server manifest.