This paper aims to give a 'state-of-the-art' introduction to the study of phonological variation in phonological theory. The discussion is structured around the question of where variation is located in the phonological component.We start with the view that variation is strictly a property of 'late'processes, which is consistent with the phonetically gradient nature of many cases of variation. We go on to discuss evidence that variation also has characteristics of 'early' phonology: it is conditioned both by morphology and by lexical idiosyncrasy. Our theoretical focus is on constraint-based approaches to variation, in OT and related theories with numerically valued weights. We pay special attention to the interaction of the lexicon with variation, an aspect of current theories that remains underdeveloped. We also provide a formal comparison of these theories with Labovian variable rules.