How can I make sense of the `else` clause of Python loops?

An if statement runs its else clause if its condition evaluates to false. Identically, a while loop runs the else clause if its condition evaluates to false.

This rule matches the behavior you described:

• In normal execution, the while loop repeatedly runs until the condition evaluates to false, and therefore naturally exiting the loop runs the else clause.
• When you execute a break statement, you exit out of the loop without evaluating the condition, so the condition cannot evaluate to false and you never run the else clause.
• When you execute a continue statement, you evaluate the condition again, and do exactly what you normally would at the beginning of a loop iteration. So, if the condition is true, you keep looping, but if it is false you run the else clause.
• Other methods of exiting the loop, such as return, do not evaluate the condition and therefore do not run the else clause.

for loops behave the same way. Just consider the condition as true if the iterator has more elements, or false otherwise.

Better to think of it this way: The else block will always be executed if everything goes right in the preceding for block such that it reaches exhaustion.

Right in this context will mean no exception, no break, no return. Any statement that hijacks control from for will cause the else block to be bypassed.

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A common use case is found when searching for an item in an iterable, for which the search is either called off when the item is found or a "not found" flag is raised/printed via the following else block:

for items in basket:
    if isinstance(item, Egg):
        break
else:
    print("No eggs in basket")  

A continue does not hijack control from for, so control will proceed to the else after the for is exhausted.

When does an if execute an else? When its condition is false. It is exactly the same for the while/else. So you can think of while/else as just an if that keeps running its true condition until it evaluates false. A break doesn't change that. It just jumps out of the containing loop with no evaluation. The else is only executed if evaluating the if/while condition is false.

The for is similar, except its false condition is exhausting its iterator.

continue and break don't execute else. That isn't their function. The break exits the containing loop. The continue goes back to the top of the containing loop, where the loop condition is evaluated. It is the act of evaluating if/while to false (or for has no more items) that executes else and no other way.