For some youth, thinking about the future -- let alone expressing aspirations for the future -- is a daunting task. This incapacity to aspire is problematic in itself, but particularly as neoliberal societies widely expect young people from adolescence onwards to "have a plan" for their own future. In our research among disadvantaged youth in Europe, we observed such dreamless predicaments countless times, prompting us to wonder: how and when do aspirations emerge? Why do they flourish or wither away over time? Why do youth from similar backgrounds, facing comparable levels of adversity, relate so differently to their future potential? Although the "capacity to aspire" is largely conditioned by one's social, economic and cultural background, it is not a given: its development depends on how individual life trajectories and the accumulated experience of social interactions become resources to explore the future in a productive way. Examining the micro-sociological processes through which the capacity to aspire unfolds is critical for understanding how young people learn to aspire and act on their aspirations in the long run. Building on insights from Appadurai, Bourdieu and research in continental Europe, this article proposes a conceptual framework for understanding how aspirations develop and wither.