1. A method comprising: identifying, by a processing device, a live content item to include in a continuous content stream; identifying, by the processing device, a portion of the live content item that is indicated as an interesting portion of the live content item based on an annotation associated with the live content item, the interesting portion corresponding to a time duration having a start time of the interesting portion and an end time of the interesting portion; computing, by the processing device, an estimated end time of a first content item included in the continuous content stream; determining that the estimated end time of the first content item occurs within the time duration; scheduling, by the processing device, the live content item to be included in the continuous content stream as a next content item to be presented for display by a client device after the first content item in response to a determination that the estimated end time of the first content item occurs within the time duration; and causing, by the processing device, the live content item to be displayed on the client device after playback of the first content item ends.