Meta-analysis is now commonly used in medical research. However there are statistical issues relating to the subject that require investigation and some are considered here, from both a methodological and a practical perspective. Each of the fixed effect and the random effects models for meta-analysis are based on certain assumptions and the validity of these is investigated. A formal test of the homogeneity assumption made in the fixed effect model may be performed. Since the test has low power, simulation was used to investigate the power under various conditions. The random effects model incorporates a between-study component of variance into the model. A likelihood based method was used to obtain a confidence interval for this variance and also to provide an interval for the overall treatment effect which takes into account the fact that the between-study variance is estimated, rather than assuming it to be known. In order to obtain confidence intervals for the treatment effect for both the fixed effect and the random effects models, distributional assumptions of normality are usually made. Such assumptions may be checked using q-q plots of the residuals obtained for each trial in the meta-analysis. In both meta-analysis models it is assumed that the weight allocated to each study is known, when in fact it must be estimated from the data. The effect of estimating the weights on the overall treatment effect estimate, its confidence intervals, the between-study variance estimate and the test statistic for homogeneity, is investigated by both analytic and simulation methods. It is shown how meta-analysis methods may be used to analyse multicentre trials of a paired cluster randomised design. Meta-analysis techniques are found to be preferable to previously published methods specifically developed for the analysis of such designs, which produce biased and potentially misleading results when a large treatment effect is present.