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Quantum key distribution (QKD) enables tap-proof exchange of cryptographic keys guaranteed by the very laws of physics. One of the last remaining roadblocks on the way towards widespread deployment of QKD is the high loss experienced during terrestrial distribution of photons, which limits the distance between the communicating parties. A viable solution to this problem is to avoid the terrestrial distribution of photons via optical fibers altogether and instead transmit them via satellite links, where the loss is dominated by diffraction instead of absorption and scattering. First dedicated satellite missions have demonstrated the feasibility of this approach, albeit with relatively low secure key rates. In order for QKD to become commercially viable, the design of future satellite missions must be focused on achieving higher key rates at lower system costs. Current satellite missions are already operating at almost optimal system parameters, which leaves little room for enhancing the key rates with currently deployed technology. Instead, fundamentally new techniques are required to drastically reduce the costs per secret bit shared between two distant parties. Entanglement-based protocols provide the highest level of security and offer several pathways for increasing the key rate by exploiting the underlying quantum correlations. In this contribution, we review the most relevant advances in entanglement-based QKD which are implementable over free-space links and thus enable distribution of secure keys from orbit. The development of satellite missions is notoriously lengthy. Possible candidates for a new generation of quantum payloads should therefore be scrutinized as early as possible in order to advance the development of quantum technologies for space applications.