Chronic kidney disease affects almost all of the organs. Recently, more attention has been paid to the kidney and the central nervous system connections. In patients on kidney replacement therapy, including kidney transplantation, there is an increased prevalence of cognitive impairment, and depression and other neurological complications, such as cerebrovascular disorders and movement disorders. Kidney transplant recipients need an assessment for the risk factors and the pattern of cognitive impairment (memory, attention and executive function decline). This enables an accurate diagnosis to be made at an earlier stage. Partial post-transplant cognitive impairment recovery is also important. Finally, doctors and patients alike face numerous ethical concerns and challenges regarding the transplantation of kidneys and other solid organs. In this review, we examined some key issues regarding cognitive impairment in kidney transplant patients. We focused on the mechanism of cognitive impairment in kidney transplant recipients, patterns of cognitive impairment; evaluation of patients with cognitive impairment for kidney transplantation, the potential impact of cognitive impairment on waitlisted and transplanted patients on patient care, non-pharmacological interventions and unmet medical needs, psychological and ethical issues in kidney transplantation, and unmet needs. As cognitive impairment in kidney transplant recipients is an underestimated, underrecognized but clinically relevant problem, screening for cognitive function before and after kidney transplantation would be worth considering in standard routine practice.