Thank you for your question, Elizabeth!
   So, to answer your question, rodents like squirrels, rats, mice, raccoons, foxes, chipmunks, and skunks are mostly the culprit. Possibly even dogs, cats, moles or voles may be digging up your plants.
   There are three major ways of approaching the problem. One or a combination of these can be implemented to "head them off at the pass."

1.    Create a physical barrier around the plants, using fencing, chicken wire, rocks, edging or placing plastic forks pointing upwards around the plants.
2. They may be looking for food in the form of grubs, a larval stage of beetles. Some ways of eliminating these are applying beneficial nematodes which kill the grubs or using milky spore bacteria. This article is an excellent source for more information on this idea.
   What's digging up your yard? | UMN Extension
   
3. Use a deterrent smell by placing herbs in pots close by or using plants close by to steer the digging animals away. At the bottom of this article there are many suggestions for plants that will detract digging animals away. 
   Cornell Cooperative Extension | Groundhog Resistant Plants (ccecolumbiagreene.org)
   

    Still another way may be to place moth balls, grated Irish Spring, predator's urine, cayenne pepper, black pepper or garlic on the soil. A small bottle of hot sauce can be added to one gallon of water and sprayed on the soil.

4. Motion detection lights can be installed as a last resort if the problem persists or if finances allow. There are a number of these on the market.

Start small in your approach and rachet your response up each time a new occurrence happens. However, I believe you will have success!

This last article is just a general overview that may have some ideas for you to use. 
Who’s that digging in my yard: Skunks, raccoons or moles? - MSU Extension