BACKGROUND: Approximately 60% to 80% of people with Parkinson's disease (PD) experience cognitive impairment that impacts on their quality of life. Cognitive decline is a core feature of the disease and can often present before the onset of motor symptoms. Cognitive training may be a useful non-pharmacological intervention that could help to maintain or improve cognition and quality of life for people with PD dementia (PDD) or PD-related mild cognitive impairment (PD-MCI). OBJECTIVES: To determine whether cognitive training (targeting single or multiple domains) improves cognition in people with PDD and PD-MCI or other clearly defined forms of cognitive impairment in people with PD. SEARCH METHODS: We searched the Cochrane Dementia and Cognitive Improvement Group Trials Register (8 August 2019), the Cochrane Central Register of Controlled Trials (CENTRAL), MEDLINE, Embase, CINAHL, and PsycINFO. We searched reference lists and trial registers, searched relevant reviews in the area and conference proceedings. We also contacted experts for clarifications on data and ongoing trials. SELECTION CRITERIA: We included randomised controlled trials where the participants had PDD or PD-MCI, and where the intervention was intended to train general or specific areas of cognitive function, targeting either a single domain or multiple domains of cognition, and was compared to a control condition. Multicomponent interventions that also included motor or other elements were considered eligible. DATA COLLECTION AND ANALYSIS: Two review authors independently screened titles, abstracts, and full-text articles for inclusion in the review. Two review authors also independently undertook extraction of data and assessment of methodological quality. We used GRADE methods to assess the overall quality of the evidence. MAIN RESULTS: Seven studies with a total of 225 participants met the inclusion criteria for this review. All seven studies compared the effects of a cognitive training intervention to a control intervention at the end of treatment periods lasting four to eight weeks. Six studies included people with PD living in the community. These six studies recruited people with single-domain (executive) or multiple-domain mild cognitive impairment in PD. Four of these studies identified participants with MCI using established diagnostic criteria, and two included both people with PD-MCI and people with PD who were not cognitively impaired. One study recruited people with a diagnosis of PD dementia who were living in long-term care settings. The cognitive training intervention in three studies targeted a single cognitive domain, whilst in four studies multiple domains of cognitive function were targeted. The comparison groups either received no intervention or took part in recreational activities (sports, music, arts), speech or language exercises, computerised motor therapy, or motor rehabilitation combined with recreational activity. We found no clear evidence that cognitive training improved global cognition. Although cognitive training was associated with higher scores on global cognition at the end of treatment, the result was imprecise and not statistically significant (6 trials, 178 participants, standardised mean difference (SMD) 0.28, 95% confidence interval (CI) -0.03 to 0.59; low-certainty evidence). There was no evidence of a difference at the end of treatment between cognitive training and control interventions on executive function (5 trials, 112 participants; SMD 0.10, 95% CI -0.28 to 0.48; low-certainty evidence) or visual processing (3 trials, 64 participants; SMD 0.30, 95% CI -0.21 to 0.81; low-certainty evidence). The evidence favoured the cognitive training group on attention (5 trials, 160 participants; SMD 0.36, 95% CI 0.03 to 0.68; low-certainty evidence) and verbal memory (5 trials, 160 participants; SMD 0.37, 95% CI 0.04 to 0.69; low-certainty evidence), but these effects were less certain in sensitivity analyses that excluded a study in which only a minority of the sample were cognitively impaired. There was no evidence of differences between treatment and control groups in activities of daily living (3 trials, 67 participants; SMD 0.03, 95% CI -0.47 to 0.53; low-certainty evidence) or quality of life (5 trials, 147 participants; SMD -0.01, 95% CI -0.35 to 0.33; low-certainty evidence). There was very little information on adverse events. We considered the certainty of the evidence for all outcomes to be low due to risk of bias in the included studies and imprecision of the results. We identified six ongoing trials recruiting participants with PD-MCI, but no ongoing trials of cognitive training for people with PDD. AUTHORS' CONCLUSIONS: This review found no evidence that people with PD-MCI or PDD who receive cognitive training for four to eight weeks experience any important cognitive improvements at the end of training. However, this conclusion was based on a small number of studies with few participants, limitations of study design and execution, and imprecise results. There is a need for more robust, adequately powered studies of cognitive training before conclusions can be drawn about the effectiveness of cognitive training for people with PDD and PD-MCI. Studies should use formal criteria to diagnose cognitive impairments, and there is a particular need for more studies testing the efficacy of cognitive training in people with PDD.