Proof-of-Work (PoW) is a popular blockchain consensus algorithm that is used in cryptocurrencies like Bitcoin in which hashing operations are repeated until the resulting hash has certain properties. This approach uses lots of computational power and energy for the sole purpose of securing the blockchain. In order to not waste energy on hashing operations that do not have any other purpose than enabling consensus between nodes and therefore securing the blockchain, Proof-of-Useful-Work (PoUW) is an alternative approach which aims to replace excessive usage of hash functions with tasks that bring additional real-world benefit, e.g. supporting scientific experiments that rely on computationally heavy simulations. This publication consists of two parts: In the first part, important properties of conventional hash-based PoW are described. In the second part, theoretical PoUW concepts such as Coinami, CoinAI and the first successful PoUW cryptocurrency Primecoin are analyzed with respects to how PoW properties can be retained while doing useful work.