With advances in scientific and clinical knowledge, stroke has evolved from a major cause of death to a chronic condition affecting the daily lives of sufferers, their relatives, and society. Post-stroke cognitive impairment (PSCI) is common even among individuals with good neurological recovery. When deciding on interventions aimed to improve the life quality of post-stroke patients, identifying those at high risk of cognitive decline proves crucial. Given the complexity of PSCI assessment, this narrative review discusses the feasibility of developing standardized criteria for selecting cognitive instruments. Potential approaches for establishing harmonized procedures for post-stroke cognitive assessment are presented depending on how the cognitive impairment is defined, the cognitive domains examined, the methods used to generalize cognitive data by components/domains, and their normalization against standardized normative samples. The prognostic value of cognitive assessment to identify patients at high risk of PSCI, functional dependence, and poor survival is also discussed. Implementing harmonized criteria for assessing the cognitive status of stroke patients could reduce the now considerable heterogeneity between studies and serve as a reliable basis for determining the prevalence and predicting the occurrence/aggravation of PSCI.