My protocol is to chill the wort in the kettle (I use an immersion chiller), then "stir it like crazy" -- it's called whirlpooling -- then wait at least an hour (I usually brew after dark, so I leave the covered kettle overnight) and siphon the wort into the fermenter.
This helps to remove both hops and hot&cold break material, which may give off-flavours to beer.
Straining hops from pellets is a nightmare, and I wouldn't advise that to anyone. I usually use hop bags, anyway, so I whirlpool&siphon only to get rid of break material.
I used to just discard the remaining ~1 l (in my setup) of liquid in the kettle, but last time I strained it, gave it a quick boil and added to the fermenter. Some people actually save that portion for later krauzening.