Aeration is important for the growth phase over the first 24 odd hrs post pitching. Sufficient oxygen in the wort will allow the yeast to drop enough pups into your wort to get the fermentation done effectively and without unwanted flavours developing.
Suffice to say that in the case of most beer styles, you can get sufficient oxygen dissolved in the wort by simply stirring vigorously for several minutes before pitching the yeast. For higher gravity worts, it's often worth while considering doing either a second aeration after about 12 hrs or direct injecting oxygen before pitching.
Most of the oxygen used with this method isn't going to remain dissolved in the wort and available to the yeast for that early phase and will simply be lost. This is mainly due to the relatively warmer temperatures of the wort (18-22 degrees or even higher).
The one thing that is a constant, is that if you don't aerate/oxygenate well before pitching, you probably won't get great results and the yeast will grudgingly slave away producing unwanted flavours in the process.
Once your beer is past the first 12-24 hrs post pitching, you don't want to be introducing any oxygen into the wort and indeed, it can end up with a poor result.
Keep in mind the warmer your wort is before pitching, the harder it is to get oxygen to stay in the wort during that aeration/oxygenation phase. Be guided by the instructions given by the company that propagates the yeast strain you're using. Every strain is different.
For the brewers who are considering direct injection of oxygen using the kits put together by the sponsoring businesses on here, especially on those big beers......go for it. Direct injection does lead to excellent results, rapid fermentation and lower FG's when you're looking for a drier finish.
If you can't/don't want to, then you'll still get great results, just with a lot more elbow grease, shaking and stirring.
Time for another IIPA.