In Java, the exception classes are organized in a hierarchy, with the base class being the Throwable class. The Throwable class has two main subclasses: Error and Exception.

The Error class represents serious errors that are usually not recoverable, such as OutOfMemoryError and StackOverflowError. These errors are usually caused by problems in the environment or in the underlying system, and cannot be handled by the program itself.

The Exception class represents less severe errors that are recoverable, such as IOException and SQLException. Exceptions are usually caused by problems in the program's logic or input, and can be handled by the program itself.

The Exception class has two main subclasses: RuntimeException and CheckedException.

1. RuntimeException is a subclass of Exception that represents errors that can occur at runtime, such as NullPointerException and ArrayIndexOutOfBoundsException. These exceptions do not need to be declared in the method signature and do not need to be caught explicitly.

2. CheckedException is a subclass of Exception that represents exceptions that must be caught or declared in the method signature. Examples of checked exceptions include IOException and ClassNotFoundException.

Here is a visual representation of the Java exception hierarchy:

Throwable
    |
    +-- Error
    |
    +-- Exception
          |
          +-- RuntimeException
          |
          +-- CheckedException

It is important to note that you can also create your own custom exception classes by extending the Exception class or one of its subclasses. This allows you to create exceptions that are specific to your program and its requirements.