Multicentre studies are common in epidemiological research aiming at identifying disease risk factors. A major advantage of multicentre over single-centre studies is that, by including a larger number of participants, they allow consideration of rare outcomes and exposures. Their multicentric nature introduces some complexities at the step of data analysis, in particular when it comes to controlling for confounding by centre, which is the focus of this tutorial. Commonly, epidemiologists use one of the following options: pooling all centre-specific data and adjusting for centre using fixed effects; adjusting for centre using random effects; or fitting centre-specific models and combining the results in a meta-analysis. Here, we illustrate the similarities of and differences between these three modelling approaches, explain the reasons why they may provide different conclusions and offer advice on which model to choose depending on the characteristics of the study. Two key issues to examine during the analyses are to distinguish within-centre from between-centre associations, and the possible heterogeneity of the effects (of exposure and/or confounders) by centre. A real epidemiological study is used to illustrate a situation in which these various options yield different results. A synthetic dataset and R and Stata codes are provided to reproduce the results.