High-dimensional multivariate integration is a difficult problem for which the Monte Carlo method is often the only viable approach. This method provides an unbiased estimator of the integral, together with a probabilistic error estimate (e.g., in the form of a confidence interval). The aim of randomized quasi-Monte Carlo (QMC) methods is to provide lower-variance unbiased estimators, also with error estimates. This talk will concentrate on one class of randomized QMC methods: randomized lattice rules.