Java supports four types of arguments: primitive data types, objects, arrays, and Strings. Primitive data types include int, float, and double. Objects are instances of classes, and can be used to call methods and access fields. Arrays are groups of data that are organized in a specific order. Strings are a special type of array that contains characters instead of numbers.   Each type of argument has its own set of rules that must be followed when passing it to a method or function. For example, primitive data types can only be passed by value, while objects can be passed by reference. Arrays can be passed by value or reference, depending on the situation. And finally, Strings can only be passed by reference. Understanding how each type of argument works is essential for passing the correct arguments to methods and functions in Java.