* Prepositional phrases: "in the garden," "with a smile," "under the table"
* Participial phrases: "walking down the street," "painted red," "running through the woods"
* Infinitive phrases: "to eat cake," "to write a novel," "to learn a new skill"
* Gerund phrases: "swimming in the ocean," "reading a book," "playing the piano"
These phrases all have a core grammatical element (like a preposition, participle, infinitive, or gerund), but they lack a subject and a verb that would make them complete sentences.