Ok, from the ATC perspective it ideally sounds like this: "approach/departure, we require xxx degrees deviation for xxx, we'll advise when able back on course". I'll ask you your new heading in order to keep you separated by means of using divergence. The sooner pilots ask, the better- our letter of agreements with next facilities require to handoff the a/c on a certain heading or established on a route; so if every a/c I'm talking to is deviating, I'd have to closely watch them and coordinate with the next controller the position of each a/c. As a result, we will limit the number of additional a/c's arriving into my airspace which will sadly will cause delays.
Please do not give your friendly ATC additional stress by turning wherever; that's said, we always allow additional space for possible deviations around puffy clouds which pilots don't inform ATC about