This paper explores the complex roles of aspirations in relation to human development, drawing upon the capability approach. The paper examines the notion of feasibility of aspirations and the impact feasibility judgements have on aspiration formation and aspiration realization, in terms of both capabilities and functionings. In particular this paper extends existing theory by building on Hart's dynamic multidimensional model of aspiration and Hart's aspiration set (2012. Aspiration, Education and Social Justice -Applying Sen and Bourdieu. London: Bloomsbury). The theorization builds on empirical work, undertaken in the UK, seeking to understand pupils' aspirations on leaving school and college at age 17-19 as well as reviewing wider empirical and theoretical literature in this field. The discussion contributes to capability theory by extending understanding regarding first, the way that aspirations are connected to capabilities and functionings, secondly, the processes by which aspirations are converted into capabilities and thirdly, how certain capabilities become functionings. The paper reflects on the criteria that inform choices about the cultivation and selection of different aspirations on individual and collective bases. In concluding the paper the question of, "how do aspirations matter?" is addressed. Ultimately, an argument is made for the need to "reclaim" a rich multi-dimensional concept of aspiration in order to pursue human development and flourishing for all.