Official statistics in the United States and the United Kingdom show a rise in poverty between the 1970's and the 1980's but scepticism has been expressed with regard to these findings. In particular, the methods employed in the measurement of poverty have been the subject of criticism. This paper re-examines three basic issues in measuring poverty: the choice of the poverty line, the index of poverty, and the relation between poverty and inequality. One general theme running through the paper is that there is a diversity of judgments which enter the measurement of poverty and that it is necessary to recognize these explicitly in the procedures adopted. There is likely to be disagreement about the choice of poverty line, affecting both its level and its structure. In this situation, we may only be able to make comparisons and not to measure differences, and the comparisons may lead only to a partial rather than a complete ordering. The first section of the paper discusses the stochastic dominance conditions which allow such comparisons, illustrating their application by reference to data for the United States. The choice of poverty measure has been the subject of an extensive literature and a variety of measures have been proposed. In the second section of the paper a different approach is suggested, considering a class of measures satisfying certain general properties and seeking conditions under which all members of the class (which includes many of those proposed) give the same ranking. Those sceptical about measures of poverty often assert that poverty and inequality are being confounded. The third section of the paper distinguishes four different viewpoints and relates them to theories of justice and views of social welfare.