The bugbear for most summer gardeners is aphids. Be it general green or blackfly or specific species such as woolly aphids, they aren't just annoying but can also be dangerous to plants.
They're carriers of disease, transporting moulds and other afflictions around our gardens, often able to do so due to their sap-sucking weakening of all the plants. One of the most important jobs in the growing season is to check plant tips, nooks in branches and under leaves for those tell-tale clumps, or before you know it you'll suddenly realise new buds have whole infestations.
There are, of course, insecticides to help you - very effective in getting rid of them, but it may have an effect on other beneficial insects in the vicinity. You could substitute them for organic versions, available in garden centres, as well as ones developed for fruit and veg use (such as Bayer Provado Fruit & Veg). Small amounts of aphids can be picked off and squashed, or even hosed off.
Otherwise look at the big picture and grow flowers that are lapped up by hoverflies, lacewings, and ladybirds, as they'll eat lots of aphid pests as a handy snack.