Annular patterns with a high degree of zonal symmetry play a prominent role in the natural variability of the atmospheric circulation and its response to external forcing. But despite their apparent importance for understanding climate variability, the processes that give rise to their marked zonally symmetric components remain largely unclear. Here the authors use simple stochastic models in conjunction with an atmospheric model and observational analyses to explore the conditions under which annular patterns arise from empirical orthogonal function (EOF) analysis of the flow. The results indicate that annular patterns arise not only from zonally coherent fluctuations in the circulation (i.e., “dynamical annularity”) but also from zonally symmetric statistics of the circulation in the absence of zonally coherent fluctuations (i.e., “statistical annularity”). It is argued that the distinction between dynamical and statistical annular patterns derived from EOF analysis can be inferred from the associated variance spectrum: larger differences in the variance explained by an annular EOF and successive EOFs generally indicate underlying dynamical annularity. The authors provide a simple recipe for assessing the conditions that give rise to annular EOFs of the circulation. When applied to numerical models, the recipe indicates dynamical annularity in parameter regimes with strong feedbacks between eddies and the mean flow. When applied to observations, the recipe indicates that annular EOFs generally derive from statistical annularity of the flow in the midlatitude troposphere but from dynamical annularity in both the stratosphere and the mid–high-latitude Southern Hemisphere troposphere.