This paper examines multidimensional poverty in Brazil in 2000 and 2010, based on the microdata of the Demographic Censuses. Our analysis is disaggregated into five classes of municipalities according to their degree of urbanisation and remoteness, highlighting wide rural–urban inequalities in the levels and dynamics of poverty. We compare estimates of traditional monetary poverty with multidimensional poverty measures based on two methods: (i) the Alkire-Foster counting identification approach; and (ii) the Permanyer two-stage poverty identification approach. The two-stage approach introduces the concepts of complementarity/substitutability within and across poverty dimensions, which enables a more precise identification of the population targeted by anti-poverty policies. All methods highlight substantial progress in poverty alleviation. In absolute terms, the reduction in the incidence of multidimensional poverty was significantly larger in the initially poorest areas—rural and intermediate municipalities, as well as those in the North and North–East regions. Important advances were made in standard of living, especially in the access to electricity, durable consumer goods and private bathroom in the households in rural and intermediate municipalities. However, remote municipalities remain relatively poorer from any perspective, facing more difficulties in reducing monetary poverty.