Given a sequence w of members of a totally ordered set, we say j is a strongly outstanding element of w if whenever i < j we have the member in position i (from the left) strictly less than the member in position j. In this case we call the member in position j a strongly outstanding value. We say j is a weakly outstanding element if the member in position i less than or equal to the member in position j whenever i < j, and call the member in position j a weakly outstanding value. We discuss the contexts in which w is a permutation, a multiset permutation, or a word over some finite alphabet. A famous theorem of Renyi states that the number of permutations of {1,2,…,k} with r strongly outstanding elements is equal to the number of such permutations with r cycles. We consider this and other properties of the outstanding elements and values of permutations, and extend them to multiset permutations and words.