The role of pancreatic beta-cells is fundamental in the control endocrine system, maintaining the blood glucose homeostais in a physiological regime, via the glucose-induced release of insulin. An increasing amount of detailed experimental evidences at the cellular and molecular biology levels have been collected on the key factors determining the insulin release by the pancreatic beta-cells. The direct transposition of such experimental data into accurate mathematical descriptions might contribute to considerably clarify the impact of each cellular component on the global glucose metabolism. Under these perspectives, we model and computer-simulate the stimulus-secretion coupling in beta-cells by describing four interacting cellular subsystems, consisting in the glucose transport and metabolism, the excitable electrophysiological behavior, the dynamics of the intracellular calcium ions, and the exocytosis of granules containing insulin. We explicit the molecular nature of each subsystem, expressing the mutual relationships and the feedbacks that determine the metabolic-electrophysiological behavior of an isolated beta-cell. Finally, we discuss the simulation results of the behavior of isolated beta-cells as well as of population of electrically coupled beta-cells in Langerhans islets, under physiological and pathological conditions, including noninsulin-dependent diabetes mellitus (NIDDM) and hyperinsulinemic hypoglycaemia (PHHI).