There are several insects (as well as other wildlife) a plant can fall victim to when growing outdoors. Here you will find explanations of common pests and methods for repelling them.
Common Insects
Spider mites
If left for too long spider mites will begin producing webs on the leaf surface, this should be addressed as soon as possible.
Thrips
Thrips are mostly recognizable from the damage they do to leaves.
Aphids
Common solutions
Neem oil
Neem oil can be added to feed water to repel insects such as spider mites or thrips. Be aware that it has a delayed effect and should be applied preventatively.
Insecticidal soap
A soap that can be used to kill insects. Less aggressive than a pesticide and some can be made using household ingredients
Predator insects
It's possible to add "good" insects that will hunt the insects you want to remove. This is only recommended for outdoor grows.
Some example predators for spider mites are Phytoseiulus persimilis and Amblyseius californicus.
For Thrips, you might use Amblyseius cucumeris.