Of all the diverse properties of segmental strings, syllable structure is the one that stress rules most often refer to. In fact, they refer to a quite specific aspect of syllable structure: syllable weight. Generally, it is this distinction between heavy and light syllables that affects the placement of stress. The richness of this problem is apparent from its ramifications. First, in many languages the notion "heavy syllable" invokes a disjunction of syllables containing a long vowel or diphthong and syllables with a short vowel but closed by a consonant. Second, though heavy syllables often attract the stress, they sometimes reject it or attract it subject to some limitations of, say, distance from a boundary. Third, the weight of some syllables may itself vary in a particular language, perhaps again under some boundary conditions. All of these issues are illustrated concretely in subsequent sections of this article. None of these observations is new, and previous work has not failed to attempt explanations of at least some of them. I know of four quite different approaches in the literature, discussed very briefly in this article.