abstract: Since the early 1980s, pancreatic beta cells have been a paradigmatic system for oscillations because of the wide range of time scales, from spiking (seconds) to bursting (tens of seconds) to slow (minutes), and the wide range of oscillating entities (membrane potential, calcium, metabolites). Because these oscillations are central for oscillations in insulin secretion, and their impairment is associated with the pathogenesis of type 2 diabetes, they have been the subject of extensive theoretical and experimental investigation, including nanoscale innovations for recording multiple readouts of cell activity. Early measurements with calcium indicators confirmed the existence of calcium oscillations predicted by the Chay-Keizer family of bursting models but were different in form than all of those predictions. This led to a wave of model revision and a new round of predictions, such as oscillations in ER calcium that have been largely confirmed. This theoretical work led to new concepts such as "phantom bursting" to account for the great plasticity of frequency by the interaction of multiple slow, negative feedback variables, and the "dual oscillator", to describe the interactions of calcium and metabolism. Predictions of this next generation of models of oscillations in glycolysis drove the invention of a FRET sensor for fructose-1,6-bisphosphate (FBP), which have been confirmed but required further revisions in the models. Through this evolution, the dynamical foundation of fold-homoclinic bursting has been stretched but shown its resilience. Ongoing iterations of model refinement and experimental testing will be discussed.