Meta-analysis enables researchers to combine the results of several studies to assess the information they provide as a whole. It has been used to give a systematic overview of many areas in which data on a possible association between an exposure and an outcome have been collected in a number of studies but where the overall picture remains obscure, both as to the existence or size of the effect. This paper outlines some innovations in meta-analysis, based on using Markov chain Monte Carlo (MCMC) techniques for implementing Bayesian hierarchical models, and compares these with a more well-known random effects (RE) model. The new techniques allow different aspects of variation to be incorporated into descriptions of the association, and in particular enable researchers to better quantify differences between studies. Both the classical and Bayesian methods are applied, in this paper, to the current collection of studies of the association between incidence of lung cancer in female never-smokers and exposure to environmental tobacco smoke (ETS), both in the home through spousal smoking and in the workplace. In this paper it is demonstrated that compared with the RE model, the Bayesian methods: (a) allow more detailed modeling of study heterogeneity to be incorporated; (b) are relatively robust against a wide choice of specifications of such information on heterogeneity; (c) allow for more detailed and satisfactory statements to be made, not only about the overall risk but about the individual studies, on the basis of the combined information. For the workplace exposure data set, the Bayesian methods give a somewhat lower overall estimate of relative risk of lung cancer associated with ETS, indicating the care that needs to be taken in using point estimates based on any one method of analysis. On the larger spousal data set the methods give similar answers. Some of the other concerns with meta-analysis are also considered. These include: consistency between different geographic areas (Asia and the United States), and our studies show that Bayesian methods permit an account of the overall picture to be taken, thus improving the ability to estimate accurately in the subgroups; and publication bias which, as shown with the spousal exposure data, may lead to an inflated excess risk.