In addition to multiple health benefits, participation in physical activity can enhance cognitive functioning. Less clear is how reducing physical activity levels affects cognition, an issue potentially addressed by bed rest studies having included cognitive tests. Detailed and reviewed here are 17 such studies, featuring 251 subjects, bed rest for 7-70 days, and tests of cognition ranging from reaction time to executive functions. The reported effects of bed rest on cognitive performance vary considerably, from a generally expected worsening to an improvement. Practice effects could be implicated in the performance improvements, and reports of worsening are often of limited interpretability or the results were not replicated. Any cognitive effects of bed rest thus remain to be established. Detrimental effects could influence the in-progress plans for human spaceflights to Mars (simulated by bed rest), and have implications for medical conditions promoting inactivity and lifestyles that are largely sedentary.