Mule ESB allows storing data in variables that can be accessed throughout a flow or entire application. Lists and maps can be defined as Mule variables similarly to how they are defined in Java. A list variable is defined using square brackets containing comma-separated values. A map variable is defined using curly brackets with key-value pairs. Values can then be retrieved from the list or map using indexes or keys, respectively. An example flow demonstrates reassigning list values and logging list and map variables.