How do you fix "Allowed memory size exhausted" in WordPress?

The fatal Allowed memory size of … bytes exhausted means a request hit the PHP memory ceiling. We raise WP_MEMORY_LIMIT in wp-config.php and the PHP memory_limit to a safe value, but the real fix is the cause: a runaway database query, a bloated import, an oversized image batch, or a plugin loop that leaks memory. We profile the request and fix the source so it doesn’t come back.