This paper considers how monetary policy produces heterogeneous effects on euro area households, depending on the composition of their income and on the components of their wealth. We first review the existing evidence on how monetary policy affects income and wealth inequality. We then illustrate quantitatively how various channels of transmission ― net interest rate exposure, inter-temporal substitution and indirect income channels ― affect individual euro area households. We find that the indirect income channel has an overwhelming importance, especially for households holding few or no liquid assets. The indirect income channel is therefore also a substantial driver of changes in consumption at the aggregate level.