Discrete choice experiments are a popular stated preference tool in health economics and have been used to address policy questions, establish consumer preferences for health and healthcare, and value health states, among other applications. They are particularly useful when revealed preference data are not available. Most commonly in choice experiments respondents are presented with a situation in which a choice must be made and with a a set of possible options. The options are described by a number of attributes, each of which takes a particular level for each option. The set of possible options is called a “choice set,” and a set of choice sets comprises the choice experiment. The attributes and levels are chosen by the analyst to allow modeling of the underlying preferences of respondents. Respondents are assumed to make utility-maximizing decisions, and the goal of the choice experiment is to estimate how the attribute levels affect the utility of the individual. Utility is assumed to have a systematic component (related to the attributes and levels) and a random component (which may relate to unobserved determinants of utility, individual characteristics or random variation in choices), and an assumption must be made about the distribution of the random component. The structure of the set of choice sets, from the universe of possible choice sets represented by the attributes and levels, that is shown to respondents determines which models can be fitted to the observed choice data and how accurately the effect of the attribute levels can be estimated. Important structural issues include the number of options in each choice set and whether or not options in the same choice set have common attribute levels. Two broad approaches to constructing the set of choice sets that make up a DCE exist—theoretical and algorithmic—and no consensus exists about which approach consistently delivers better designs, although simulation studies and in-field comparisons of designs constructed by both approaches exist.