There’s a lot of controversy around the role of citrus in the garden: Can it be composted? Will it deter pests? It turns out that while citrus is probably not altogether harmful to your garden, and can—in limited circumstances—be helpful, it's very likely not worth bothering with.
Citrus is problematic as a compost ingredient and mulch
Worms don’t love citrus, and if you are vermicomposting, you don’t want to work against the proletariat. However, the idea that citrus doesn’t compost well is a myth—everything on Earth will eventually break down, and citrus will do so at roughly the same rate as other kitchen scraps, although it’s advised to separate the seeds, fruit, and pith from the peel before you do. Not only is this more work than I’m willing to do for my compost, but it points to one of the problems with composting citrus: The good stuff is largely in the fruit, which will be gone by the time you compost. The seeds will ferment and sprout, and the peels deter your composting worms, so there's no real upside.
While it is also true that citrus fruit is a good source of nitrogen, phosphorus, and potassium, the building blocks of your soil, it won’t be a shock that it is highly acidic. That can shift your soil pH, and that’s not a good idea, unless you are using it in limited ways, and under plants that want that acidity, like blueberries or azaleas. Even in those cases, you want to monitor the pH, because while those plants will enjoy a higher pH, it’s only a slightly higher range. After that, the pH works against your plants' objectives.
Citrus can deter pests, but only at levels that you won’t achieve with kitchen scraps
There was a summer when a neighbor's cat had taken up residence in my yard and started using the vegetable garden as a litter box, and as a preventative measure, she spread citrus peels all across my garden. This, too, is an old wives' tale. Citrus, it’s true, can deter some pests, like rats and mice. They don’t enjoy citrus oil, which is in the peels. However, the concentration of oil needed to be effective is higher than you will achieve by just throwing peels around, even indoors. Moreover, those peels dry out quickly, and then the oil is non-existent. Also, the fact that the compound in citrus peels, d-limonene, can be toxic if ingested by animals was concerning in this case. For what it’s worth, the cat was undeterred, and I had a rotten garden year.
I've also seen citrus mentioned as a slug deterrent, but this is also largely a myth. Slugs are attracted to citrus (slugs are attracted to most edibles), so you can use it as a makeshift trap and then dispose of the peel and the slugs. If trapping is the goal, though, beer traps work more effectively without negatively affecting the garden bed. Ultimately though, as someone who lives in a place where slugs are prolific, your best defense against slugs is Sluggo, which is, thankfully, organic.
While d-limonene is part of many mosquito and tick repellents and can be effective, the concentration you'd need to be effective would require a commercial juice production in your home.
Finding gardeners who practice using citrus in gardens is hard
For two weeks, I polled gardeners near and far, including many master gardeners, published authors of respected gardening books, and owners of nurseries, and not a single one had ever used citrus in the garden. I couldn’t find a single person with hands-on experience, good or bad. This is likely because whatever benefit you might derive from citrus is easily had with other modern garden materials.