Studies suggest that patients with hematological malignancies undergoing allogeneic hematopoietic stem cell transplantation (HSCT) are at risk for cognitive decline and long-term cognitive dysfunction. To address this issue, a randomized controlled intervention trial on the effect of physical exercise on cognition is conducted. In addition, the impact on psychological and physical health outcomes such as depression, fatigue, health-related quality of life and physical fitness is evaluated. A healthy control group matched to the patients on age, gender, and education will be included to both control for practice effects on neuropsychological measures and allow additional comparisons on self-report measures. The healthy control group will undergo neuropsychological testing and questionnaire survey at baseline and 4 months. Demographic data will be collected from all study participants at baseline. Medical data will be collected from patients at all time points. Results may benefit patients who suffer from disease- or treatment-associated cognitive change.