Which event should a developer use to detect when the browser's native back or forward button is clicked?

The popstate event is specifically designed to handle changes to the active history entry in the browser, which occurs when the user navigates back or forward in their browsing history. This event is triggered when the user clicks the native back or forward buttons, allowing developers to respond accordingly, for example, by updating the displayed content to match the new history state.

It is important to understand that the popstate event is part of the History API in JavaScript, which allows for dynamic page navigation without requiring a full page reload. When the state associated with the history entry changes either due to navigation or programmatically with history.pushState() or history.replaceState(), the popstate event provides a way to manage these transitions smoothly.

The other choices do not serve this purpose. The navigate event is not standard and may not be consistently implemented across browsers, while pushstate is a method used to add a new state to the history stack but does not detect navigation events. The change event relates more to form elements and their value changes, rather than navigation actions. Thus, popstate is the most appropriate choice for detecting when a user interacts with the browser's back or forward buttons.