In recent years, the number of studies examining mind wandering has increased considerably, and research on the topic has spread widely across various domains of psychological research. Although the term “mind wandering” has been used to refer to various cognitive states, researchers typically operationalize mind wandering in terms of “task-unrelated thought” (TUT). Research on TUT has shed light on the various task features that require people’s attention, and on the consequences of task inattention. Important methodological and conceptual complications do persist, however, in current investigations of TUT. As we argue, these complications may be dampening the development of a more nuanced scientific account of TUT. Here, we outline three of the more prominent methodological and conceptual complications in the literature on TUT, and we discuss potential directions for researchers to take as they move forward in their investigations of TUT.