Electroencephalography-based brain-computer interfaces (BCI) that allow the control of robotic devices to support stroke patients during upper limb rehabilitation are increasingly popular. Hand rehabilitation is focused on improving dexterity and fine motor control and is a core approach for helping stroke survivors regain activities of daily living. This systematic review examines recent developments in BCI-robotic systems for hand rehabilitation and identifies evidence-based clinical studies on stroke patients. A search for January 2010-October 2019 articles using Ovid MEDLINE, Embase, PEDro, PsycINFO, IEEE Xplore and Cochrane Library databases was performed. The selection criteria included BCI-hand robotic systems for rehabilitation in various development stages involving tests on healthy human subjects or stroke survivors. Data fields include those related to study design, participant characteristics, technical specifications of the system, and clinical outcome measures. 30 studies were identified as eligible for qualitative review and among these, 11 studies involved testing a BCI-hand robot on chronic and subacute stroke patients. Statistically significant improvements in motor assessment scores relative to controls were observed for two BCI-hand robot interventions. The degree of robot control for the majority of studies was limited to triggering the device to perform grasping or pinching movements using motor imagery. Most employed a combination of kinaesthetic and visual response via the robotic device and display screen, respectively, to match feedback to motor imagery. Most studies on BCI-robotic systems for hand rehabilitation report systems at prototype or pre-clinical stages of development. Some studies report statistically significant improvements in functional recovery after stroke, but there is a need to develop a standard protocol for assessing technical and clinical outcomes so that the necessary evidence base on efficiency and efficacy can be developed.