Stable isotope analysis has emerged as one of the primary means for examining the structure and dynamics of food webs, and numerous analytical approaches are now commonly used in the field. Techniques range from simple, qualitative inferences based on the isotopic niche, to Bayesian mixing models that can be used to characterize food-web structure at multiple hierarchical levels. We provide a comprehensive review of these techniques, and thus a single reference source to help identify the most useful approaches to apply to a given data set. We structure the review around four general questions: (1) what is the trophic position of an organism in a food web?; (2) which resource pools support consumers?; (3) what additional information does relative position of consumers in isotopic space reveal about food-web structure?; and (4) what is the degree of trophic variability at the intrapopulation level? For each general question, we detail different approaches that have been applied, discussing the strengths and weaknesses of each. We conclude with a set of suggestions that transcend individual analytical approaches, and provide guidance for future applications in the field.