There are several common operations that are performed on various data structures:

1. Insertion: This operation involves adding a new element to the data structure.
2. Deletion: This operation involves removing an element from the data structure.
3. Searching: This operation involves finding an element within the data structure.
4. Traversal: This operation involves visiting every element within the data structure in a specific order.
5. Sorting: This operation involves rearranging the elements within the data structure in a specific order.
6. Merging: This operation involves combining two or more data structures into a single structure.
7. Splitting: This operation involves dividing a single data structure into two or more structures.
8. Reversing: This operation involves reversing the order of the elements within the data structure.
9. Rotating: This operation involves shifting the elements within the data structure by a certain number of positions.
10. Shuffling: This operation involves randomly rearranging the elements within the data structure.