Subjects in randomized controlled trials do not always comply to the treatment condition they have been assigned to. This may cause the estimated effect of the intervention to be biased and also affect efficiency, coverage of confidence intervals, and statistical power. In cluster randomized trials non-compliance may occur at the subject level but also at the cluster level. In the latter case, all subjects within the same cluster have the same compliance status. The purpose of this study is to investigate the statistical implications of non-compliance in cluster randomized trials. A simulation study was conducted with varying degrees of non-compliance at either the cluster level or subject level. The probability of non-compliance depends on a covariate at the cluster or subject level. Various realistic values of the intraclass correlation coefficient and cluster size are used. The data are analyzed by intention to treat, as treated, per protocol and the instrumental variable approach. The results show non-compliance may result in downward biased estimates of the intervention effect and an under- or overestimate of its standard deviation. The coverage of the confidence intervals may be too small, and in most cases, empirical power is too small. The results are more severe when the probability of non-compliance increases and the covariate that affects compliance is unobserved. It is advocated to avoid non-compliance. If this is not possible, compliance status and covariates that affect compliance should be measured and included in the statistical model.