How can the PHP datetime functions be effectively used to manipulate dates in different formats?

To manipulate dates in different formats using PHP datetime functions, you can use the `DateTime` class along with its various methods to format, modify, and manipulate dates. You can create a `DateTime` object with the date you want to work with, then use methods like `format()` to output the date in a specific format, `modify()` to add or subtract time intervals, and `diff()` to calculate the difference between two dates.

$date = new DateTime('2022-01-01');
echo $date->format('Y-m-d'); // Output: 2022-01-01

$date->modify('+1 day');
echo $date->format('Y-m-d'); // Output: 2022-01-02

$futureDate = new DateTime('2022-12-31');
$interval = $date->diff($futureDate);
echo $interval->format('%a days'); // Output: 363 days