The guitarist, finger-picking, was extraordinary. He was not impressed with their competing. He was not impressed with them competing. Grandpa enjoyed his grandchildren's running and laughing. Grandpa enjoyed his grandchildren, running and laughing.
Gerunds always function as nouns, but infinitives often also serve as nouns.
Deciding which to use can be confusing in many situations, especially for people whose first language is not English. Confusion between gerunds and infinitives occurs primarily in cases in which one or the other functions as the direct object in a sentence. In English some verbs take gerunds as verbal direct objects exclusively while other verbs take only infinitives and still others can take either. Many such verbs are listed below, organized according to which kind of verbal direct object they take. With many of the verbs that follow the object, the use of the gerund indicates continuous action while the use of the simple verb indicates a one-time action.