Providing a computer program product, system, and method for logging updates to monitored data sets in a storage. A request is received to monitor changes to a monitored data set comprising one of the data sets in the storage. A determination is made of tracks in the storage in which the data set is stored. The determined tracks are indicated in monitored tracks. Updates to the storage are received and a determination is made as to whether the updates are for the monitored tracks. The updates are logged in response to determining that updates are for the monitored tracks. A determination is made of new tracks added to the monitored data set and the determined new tracks are indicated in the monitored tracks.