We present an overview of the evolution of the United Nations General Assembly, its most important achievements and remaining weaknesses and relevance. It is argued that the UN Charter should be amended to introduce a system of weighted voting, to better reflect the relative significance and influence of its 193 members. A proposal is put forward that uses three variables to arrive at a set of weights for membership in the General Assembly: (i) population size, to reflect each member’s accumulated demographic history so that countries with larger populations will have a larger voice; (ii) the size of the member’s economy; and (iii) a UN membership factor that is equal for all countries. For the GDP variable, the weighted average of GDP at market prices and GDP at PPP rates is used. The merits and limitations of such a scheme are analyzed and a gradual system of direct election of Assembly members is proposed. The chapter also presents the UN Charter’s Articles 9–11 on General Assembly composition, functions and powers and discusses how these Articles should be amended to reflect the new system of weighted voting and the enhanced powers that are envisaged for the Assembly under a revised Charter.