Cognition can unfold with little regard to the events taking place in the environment, and such self-generated mental activity poses a specific set of challenges for its scientific analysis in both cognitive science and neuroscience. One problem is that the spontaneous onset of self-generated mental activity makes it hard to distinguish the events that "control the occurrence of the experience" from those "processes that ensure the continuity of an internal train of thought once initiated". This review demonstrates that a distinction between process and occurrence (a) provides theoretical clarity that has been absent from current discussions of self-generated mental activity, (b) affords conceptual leverage on seemingly disparate results associating the state with both domain-general processes and task error, and (c) draws attention to important questions for understanding unconstrained thought in contexts such as psychopathology and education. It is suggested that identifying the moment that self-generated mental events begin is a necessary next step in moving toward a testable account of why the mind has evolved to neglect the present in favor of ruminations on the past or imaginary musings of what may yet come to pass. (Contains 4 figures, 1 table and 5 footnotes.)