I have inherited a project that has some huge switch statement blocks, with some containing up to 20 cases. What is a good way to rewrite these?
Depending on what the switch statement is evaluating, you may want to refactor it using the Strategy Pattern. Take a look at this post for an example of replacing a switch on enum values with separate classes to handle each function.
It also may be that using the switch with 20 cases may actually be the best course of action for it. As long as it's readable and each result clearly conveys what the action is there's no need to really refactor it.