In the last year, COVID-19 has tested both advanced and developing economies. Within such a context, the global learning crisis is expected to increase due to difficulties in accessing technology or in receiving learning support. Such a huge need, globally identified with the Sustainable Development Goal number 4 (hereafter SDG 4), implies the need for large-scale solutions from governments around the world, especially in terms of dedicated financial resources. In this context, the impact-investing sector offers an innovative financial tool, i.e., impact bonds (IBs), which are widely applied in the education sector, even if their limitations and potentials remain unexplored in academia. Based on these considerations, our work explores whether and how IBs can contribute to funding and improving educational outcomes, with a focus on their potentials in the post-COVID world. This study adopts a qualitative approach by performing a case study analysis of four IBs. Our pilot analysis is based on the following key dimensions: (i) partnerships and contractual arrangements; (ii) financial terms; and (iii) measurement and impact. The results offer interesting insights by deriving a preliminary model on the role of IBs in the post-COVID-19 world.