Some fruits more than others are at their best when left to mature on the tree. I'm also guessing that some fruit keeps better on the tree than if they are harvested and stored, unless you have special storage facilities.
My question is how to harvest and/or treat fruit for the best eating quality. One issue for me is how to select fruit on the tree that is mature/ready for picking. I'm sure that it depends on the fruit and non-commercial growers have much more leeway for getting that perfect fruit, so I'd like to hear how people do this.
I was never able to pick good apricots from the tree and noted that the best tasting were the ones that had fallen, so I rigged up a cloth to catch the fruit when it fell. I couldn't see/feel any difference between the fruit still on the tree and the fruit I caught in the cloth, but the fallen apricots were way juicier and sweeter. I do the same with my mangos now - in part because because of the numbers and the trees are so high that it would be a major undertaking to check the individual fruits.
Citrus, I used to check with a gentle tug but the mandarins often sounded like I was tearing something inside. I now rotate the fruit 90 degrees to the stem and pull even more gently. That seems to work well with Valencia and Mandarin oranges and grapefruit but doesn't work with Key limes which are at their best when still green, before they yellow and they are far from their best if they are left to fall from the tree.
I also seem to find that the citrus at the top and on the South side of the trees seem to mature first, presumably because of sun exposure.