In schizophrenia, impairments in neurocognition (NC) and social cognition (SC) are associated with reduced functional capacity (FC) and poor real-world functioning (RWF). In this semi-systematic review, we examined this association across a range of research questions. We conducted a systematic search in Embase and MEDLINE from 2005 to 2019, and conducted additional pragmatic searches. After screening of titles, abstracts and full-texts, we included 564 citations, of which 44 (26 primary studies, 15 systematic reviews and 3 narrative reviews) were prioritized for reporting. Both NC and SC were significantly associated with functioning, with slightly stronger association for SC. Effect sizes were generally larger for FC than for RWF. NC showed stronger associations with occupational functioning and independent living, and SC with social functioning. Baseline cognition predicted long-term RWF up to 20 years of follow-up, though long-term data were limited for SC. Cognitive remediation improved RWF functioning, especially when it was combined with psychosocial rehabilitation. SC mediated the relationship of NC with functioning. Negative symptoms appeared to mediate and moderate the association of cognition with functioning. Other factors involved included severity of cognitive dysfunction, metacognition, depression and choice of RWF instrument. We discuss potential implications for studies of pharmacological cognitive interventions in schizophrenia - the relevance of both NC and SC, the advantage of adjunctive psychosocial rehabilitation, the role of relevant moderating and mediating variables, and the challenges with RWF instrument selection. Successful cognitive interventions could allow patients with schizophrenia to improve their potential for community functioning.