After stroke, dynamic changes take place from necrotic-apoptotic continuum, inflammatory response to poststroke neurogenesis, and remodeling of the network. These changes and baseline brain pathology such as small vessel disease (SVD) and amyloid burden may be associated with the occurrence of early or late poststroke cognitive impairment (PSCI) or dementia (PSD), which affect not only stroke victims but also their families and even society. We reviewed the current concepts and understanding of the pathophysiology for PSCI/PSD and identified useful tools for the diagnosis and the prediction of PSCI in serological, CSF, and image characteristics. Then, we untangled their relationships with blood pressure (BP) and blood pressure variability (BPV), important but often overlooked risk factors for PSCI/PSD. Finally, we provided evidence for the modifying effects of BP and BPV on PSCI as well as pharmacological and non-pharmacological interventions and life style modification for PSCI/PSD prevention and treatment.