We illustrate and discuss several general issues associated with the random component of utility, or more generally “unobserved variability”. We posit a general conceptual framework that suggests a variance components view as an appropriate structure for unobserved variability. This framework suggests that “unobserved heterogeneity” is only one component of unobserved variability; hence, a more general view is required. We review a considerable amount of empirical research that suggests that random components are unlikely to be independent of systematic components, and random component variances are unlikely to be constant between or within individuals, time periods, locations, etc. We also review evidence that random components are functions of (elements of) systematic components. The latter suggests considerable caution in the use and interpretation of complex choice model specifications, in particular recently introduced forms of random parameter models that purport to estimate distributions of preference parameters. Several areas for future research are identified and discussed.