BACKGROUND: Outwardly directed aggressive behaviour in people with intellectual disabilities is a significant issue that may lead to poor quality of life, social exclusion and inpatient psychiatric admissions. Cognitive and behavioural approaches have been developed to manage aggressive behaviour but the effectiveness of these interventions on reducing aggressive behaviour and other outcomes are unclear. This is the third update of this review and adds nine new studies, resulting in a total of 15 studies in this review. OBJECTIVES: To evaluate the efficacy of behavioural and cognitive-behavioural interventions on outwardly directed aggressive behaviour compared to usual care, wait-list controls or no treatment in people with intellectual disability. We also evaluated enhanced interventions compared to non-enhanced interventions. SEARCH METHODS: We used standard, extensive Cochrane search methods. The latest search date was March 2022. We revised the search terms to include positive behaviour support (PBS). SELECTION CRITERIA: We included randomised and quasi-randomised trials of children and adults with intellectual disability of any duration, setting and any eligible comparator. DATA COLLECTION AND ANALYSIS: We used standard Cochrane methods. Our primary outcomes were change in 1. aggressive behaviour, 2. ability to control anger, and 3. adaptive functioning, and 4. ADVERSE EFFECTS: Our secondary outcomes were change in 5. mental state, 6. medication, 7. care needs and 8. quality of life, and 9. frequency of service utilisation and 10. user satisfaction data. We used GRADE to assess certainty of evidence for each outcome. We expressed treatment effects as mean differences (MD) or odds ratios (OR), with 95% confidence intervals (CI). Where possible, we pooled data using a fixed-effect model. MAIN RESULTS: This updated version comprises nine new studies giving 15 included studies and 921 participants. The update also adds new interventions including parent training (two studies), mindfulness-based positive behaviour support (MBPBS) (two studies), reciprocal imitation training (RIT; one study) and dialectical behavioural therapy (DBT; one study). It also adds two new studies on PBS. Most studies were based in the community (14 studies), and one was in an inpatient forensic service. Eleven studies involved adults only. The remaining studies involved children (one study), children and adolescents (one study), adolescents (one study), and adolescents and adults (one study). One study included boys with fragile X syndrome. Six studies were conducted in the UK, seven in the USA, one in Canada and one in Germany. Only five studies described sources of funding. Four studies compared anger management based on cognitive behaviour therapy to a wait-list or no treatment control group (n = 263); two studies compared PBS with treatment as usual (TAU) (n = 308); two studies compared carer training on mindfulness and PBS with PBS only (n = 128); two studies involving parent training on behavioural approaches compared to wait-list control or TAU (n = 99); one study of mindfulness to a wait-list control (n = 34); one study of adapted dialectal behavioural therapy compared to wait-list control (n = 21); one study of RIT compared to an active control (n = 20) and one study of modified relaxation compared to an active control group (n = 12). There was moderate-certainty evidence that anger management may improve severity of aggressive behaviour post-treatment (MD -3.50, 95% CI -6.21 to -0.79; P = 0.01; 1 study, 158 participants); very low-certainty evidence that it might improve self-reported ability to control anger (MD -8.38, 95% CI -14.05 to -2.71; P = 0.004, I = 2%; 3 studies, 212 participants), adaptive functioning (MD -21.73, 95% CI -36.44 to -7.02; P = 0.004; 1 study, 28 participants) and psychiatric symptoms (MD -0.48, 95% CI -0.79 to -0.17; P = 0.002; 1 study, 28 participants) post-treatment; and very low-certainty evidence that it does not improve quality of life post-treatment (MD -5.60, 95% CI -18.11 to 6.91; P = 0.38; 1 study, 129 participants) or reduce service utilisation and costs at 10 months (MD 102.99 British pounds, 95% CI -117.16 to 323.14; P = 0.36; 1 study, 133 participants). There was moderate-certainty evidence that PBS may reduce aggressive behaviour post-treatment (MD -7.78, 95% CI -15.23 to -0.32; P = 0.04, I = 0%; 2 studies, 275 participants) and low-certainty evidence that it probably does not reduce aggressive behaviour at 12 months (MD -5.20, 95% CI -13.27 to 2.87; P = 0.21; 1 study, 225 participants). There was low-certainty evidence that PBS does not improve mental state post-treatment (OR 1.44, 95% CI 0.83 to 2.49; P = 1.21; 1 study, 214 participants) and very low-certainty evidence that it might not reduce service utilisation at 12 months (MD -448.00 British pounds, 95% CI -1660.83 to 764.83; P = 0.47; 1 study, 225 participants). There was very low-certainty evidence that mindfulness may reduce incidents of physical aggression (MD -2.80, 95% CI -4.37 to -1.23; P < 0.001; 1 study; 34 participants) and low-certainty evidence that MBPBS may reduce incidents of aggression post-treatment (MD -10.27, 95% CI -14.86 to -5.67; P < 0.001, I = 87%; 2 studies, 128 participants). Reasons for downgrading the certainty of evidence were risk of bias (particularly selection and performance bias); imprecision (results from single, often small studies, wide CIs, and CIs crossing the null effect); and inconsistency (statistical heterogeneity). AUTHORS' CONCLUSIONS: There is moderate-certainty evidence that cognitive-behavioural approaches such as anger management and PBS may reduce outwardly directed aggressive behaviour in the short term but there is less certainty about the evidence in the medium and long term, particularly in relation to other outcomes such as quality of life. There is some evidence to suggest that combining more than one intervention may have cumulative benefits. Most studies were small and there is a need for larger, robust randomised controlled trials, particularly for interventions where the certainty of evidence is very low. More trials are needed that focus on children and whether psychological interventions lead to reductions in the use of psychotropic medications.