In what situations is it appropriate to use unchecked exceptions in code?

Unchecked exceptions in Java are exceptions that do not require mandatory catching or declaring in the method signature (for example, RuntimeException and its subclasses).

They are appropriate to use when:

• The error results from a programming mistake that cannot or should not be explicitly handled (for example, NullPointerException, IllegalArgumentException).
• The exception indicates a state that does not make sense to recover in the calling code.
• You want to simplify the API by not forcing users to handle exceptions that are typically not recoverable.

Example:

public int divide(int a, int b) {
    if (b == 0) {
        throw new IllegalArgumentException("Division by zero");
    }
    return a / b;
}

Here, IllegalArgumentException is an unchecked exception signaling incorrect usage of the method.