most significantly Immanuel Wallerstein draws on, extends, challenges dependency theory

Wikipedia, section on dependency theory:

World-systems analysis builds upon but also differs fundamentally from dependency theory. While accepting world inequality, the world market and imperialism as fundamental features of historical capitalism, Wallerstein broke with orthodox dependency theory’s central proposition. For Wallerstein, core countries do not exploit poor countries for two basic reasons.

Firstly, core capitalists exploit workers in all zones of the capitalist world economy (not just the periphery)== and therefore, ==the crucial redistribution between core and periphery is surplus value, not “wealth” or “resources” abstractly conceived==. Secondly, ==core states do not exploit poor states, as dependency theory proposes, because capitalism is organised around an inter-regional and transnational division of labor rather than an international division of labour.== Thirdly, economically relevant ==structures such as metropolitan regions, international unions and bilateral agreements tend to weaken and blur out the economic importance of nation-states and their borders.23

During the Industrial Revolution, for example, English capitalists exploited slaves (unfree workers) in the cotton zones of the American South, a peripheral region within a semiperipheral country, United States.24

From a largely Weberian perspective, Fernando Henrique Cardoso described the main tenets of dependency theory as follows:

• There is a financial and technological penetration of the periphery and semi-periphery countries by the developed capitalist core countries.
• That produces an unbalanced economic structure within the peripheral societies and between them and the central countries.
• That leads to limitations upon self-sustained growth in the periphery.
• That helps the appearance of specific patterns of class relations.
• They require modifications in the role of the state to guarantee the functioning of the economy and the political articulation of a society, which contains, within itself, foci of inarticulateness and structural imbalance.25

Dependency and world system theory propose that the poverty and backwardness of poor countries are caused by their peripheral position in the international division of labor. Since the capitalist world system evolved, the distinction between the central and the peripheral states has grown and diverged. In recognizing a tripartite pattern in the division of labor, world-systems analysis criticized dependency theory with its bimodal system of only cores and peripheries.