Satisfactory patterns of Human Development require that the process of expansion of capabilities is sustained. This paper analyses the relationship between inequality and sustainability from three perspectives: macro-economic sustainability; environmental sustainability; and political sustainability. It argues that greater inequality makes it more difficult to achieve each of the three. In the first two cases, it is vertical inequality that is relevant, and in the third horizontal inequality.  In the case of environmental sustainability there is a two-way link such that worsening environmental conditions tend to be most adverse for the poorest and consequently raise inequality, while a substantial reduction in inter and intra-country inequality appears to be necessary for any substantial reduction in growth of output (and consequently an improvement in environment from this source) to be acceptable. The paper also explores some conflicts and complementarities between the three types of sustainability. Sustainability of Human Development requires that all three types of sustainability are realized.