Gerunds and infinitives are verb forms that can function as nouns. A gerund is a verb form ending in "-ing" that can follow adjectives, verbs, and prepositions. An infinitive is "to + verb" and can be the subject or object of a sentence. Both gerunds and infinitives can be subjects, direct objects, or objects of prepositions. Certain verbs like "begin" and "want" can be followed by either gerunds or infinitives.