With the rapid growth of Internet of Things (IoT) applications, there's a big demand for more processing power and resources in devices. Mobile Edge Computing (MEC) looks promising for enhancing performance and reducing costs by offloading the computing work of IoT to MEC servers. However, the current methods for offloading have issues with privacy and security during the transfer of data and programs. To tackle this, recent developments have introduced secure offloading methods using Blockchain technology, which helps to make MEC more secure by building trust between nodes, improving how edges are authenticated and accessed, and stopping unauthorized access to devices. This paper reviews these Blockchain-based offloading methods for different MEC settings. It starts by explaining the key ideas in offloading and Blockchain, then it sorts the Blockchain-based offloading methods by the algorithms they use. It also compares the offloading methods in each group and ends with a discussion and comparison of the different techniques, tools, and metrics used in these methods.