Proof-of-Work (PoW) blockchains have emerged as a robust and effective consensus mechanism in open environments, leading to widespread deployment with numerous cryptocurrency platforms and substantial investments. However, the commonly deployed PoW implementations are all based on solving cryptographic puzzles. Researchers have been pursuing the compelling idea of replacing cryptopuzzles with useful computing tasks for over a decade, in face of the substantial computational capacity of blockchain networks and the global pursuit of a more sustainable IT infrastructure. In this study, we conduct a comprehensive analysis of the prerequisites for alternative classes of tasks. We provide insight into the effect of introducing "usefulness" and of transitioning to task classes other than cryptopuzzles. Having distilled the prerequisites, we use them to examine proposed designs from existing literature. Finally, we discuss pertinent techniques and present research gaps in the current state-of-the-art.