The proliferation of resource-constrained devices has become prevalent across various digital applications, including smart homes, smart healthcare, and smart transportation, among others. However, the integration of these devices brings many security issues. To address these concerns, Blockchain technology has been widely adopted due to its robust security characteristics, including immutability, cryptography, and distributed consensus. However, implementing blockchain within these networks is highly challenging due to the limited resources of the employed devices and the resource-intensive requirements of the blockchain. To overcome these challenges, a multitude of researchers have proposed lightweight blockchain solutions specifically designed for resource-constrained networks. In this paper, we present a taxonomy of lightweight blockchain solutions proposed in the literature. More precisely, we identify five areas within the "lightweight" concept, namely, blockchain architecture, device authentication, cryptography model, consensus algorithm, and storage method. We discuss the various methods employed in each "lightweight" category, highlighting existing gaps and identifying areas for improvement. Our review highlights the missing points in existing systems and paves the way to building a complete lightweight blockchain solution for networks of resource-constrained devices.