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Straight or meandering tunnels (hence the name, miners) are made in the leaf. These patches eventually dry up and turn brown.
Little white larvae eat out these areas, they can often still be seen in the leaf. There are different types of miner, some specific to certain plants, such as apple, holly and beech miners.
None, except looking unsightly.
Organic - pick off infected leaves if you want and squash any larvae found.
Chemical - you can spray with a contact insecticide when the damage is first seen. However, if the mined area has dried up and gone papery, then the leaf miner has already hatched and left so there is no need to spray.