Randomised trials are viewed as the gold standard for evaluating interventions. Depending on the intervention as well as other logistical factors, individuals or group of individuals may be randomised. The former is known as individual randomised controlled trials (RCTs) and the latter as cluster randomised trials (CRTs). CRTs offer advantages such as administrative convenience and reduction of contamination between trial groups but analysis is more complex than that for RCTs, because of the correlations between participants in the same cluster. When non-adherence to treatment occurs in the sense that some participants do not receive the randomly assigned treatment, confounding may exist as there may be common factors influencing treatment received and outcome. Consequently, the intention-to-treat approach, which compares outcomes between the groups as randomised, assesses the effect of being randomised to treatment rather than the causal treatment effect (effect of receiving the treatment). Ad-hoc methods often used to attempt to estimate the causal effect of treatment received such as per-protocol (PP) and as-treated (AT) approaches are likely to provide biased estimates because the assumptions necessary for those approaches to be unbiased are in general implausible. There exists extensive literature on estimating causal treatment effects from RCTs with non-adherence, but not as much for CRTs. Instrumental variables (IV) methods have the advantage, over other causal methods, of accommodating settings where there are unmeasured confounders when making causal inference. This thesis contributes to the literature on the estimation of causal treatment effects in CRTs where there is non-adherence to treatment and focuses on IV-based methods. I first ascertained the current practice of reporting and addressing nonadherence when causal treatment effects are of interest in CRTs via a systematic review of 123 CRT reports. Non-adherence was reported in about half of the CRTs, of which a third were interested in the causal treatment effect. All of the reviewed CRTs that reported adherence-adjusted estimates performed either PP or AT, without discussing the plausibility of the very strong assumptions necessary for such analyses to result in unbiased causal treatment estimates. No study estimated the local average treatment effect (LATE), that is the average treatment effect on those that would comply with the random allocated treatment, or any other appropriate statistical methods for unbiased causal estimation. In many clinical settings, the relevant causal question is whether treatment has an effect among those who are willing to take it, which would be quantified by the LATE. Hence the thesis focuses on this estimand, starting with an introduction and assessment of the performance of IV-based methods for estimating LATE at either cluster level (CL) or individual level (IL) through simulations under the required identification assumptions for LATE. I also perform sensitivity analyses for IL-LATE estimation and illustrate those methods using two real CRTs. The methods include two-stage least squares (TSLS) based on CL outcome summaries and the Wald estimator with the Schochet-Chiang standard error to estimate CL-LATE, and the Wald estimator, TSLS with robust cluster standard errors, TSLS with Moulton's standard errors and the Bayesian multilevel mixture modelling for estimating ILLATE. I conduct extensive simulations and illustrate the methods using real CRTs data. I demonstrate that TSLS is attractive for the estimation of CL-LATE and IL-LATE but is inefficient. This inefficiency may be reduced through covariate adjustment. The Bayesian multilevel mixture modelling is also attractive due to its flexibility and performs well particularly when non-adherence is at the individual level and the intracluster correlation coefficient for outcome is large. Stata and R codes are provided to facilitate implementation by trial investigators. I conclude by making some recommendations about how to estimate CL-LATE and IL-LATE to improve the quality of analysis when estimating causal treatment effects in the presence of non-adherence in CRTs.