Poverty analysis is in the midst of a multidimensional “turn” due, in part, to the growing awareness of the limitations of relative income measures of poverty. In this paper, we argue that the conceptualisation of poverty remains a neglected aspect of this multidimensional turn to date, and demonstrate that the counter-intuitive results which flow from relative income analyses are not problems of measurement, but are entirely consistent with the conceptualisation of poverty under Peter Townsend’s dominant Poverty as Relative Deprivation framework. In response to these problems we articulate an alternative framework, Poverty as Capability Deprivation, drawing on Amartya Sen’s capability approach, and argue that this provides more persuasive explanations as to why some nations have greater poverty than others and why poverty remains a problem even in the richest nations.