The quantitative study of beta-cell function has relied on mathematical models for almost 40 years. During the last decades, the initial elaborate models have been simplified with the aim of obtaining mathematical methods suitable for the assessment of beta-cell function in an individual from an intravenous test. In more recent times, modelling methods have been proposed for analysing oral glucose tolerance tests or meal tests. In this review, we describe these methods with particular emphasis on an approach we have developed. We discuss the relevance of potentiation of insulin secretion in an oral glucose test, which our model has reintroduced after the historical models. We provide evidence on the validity of the method and illustrate significant applications. We emphasize the importance of quantifying beta-cell function through multiple indices and highlight how our approach has provided new insight on the relationships between beta-cell function and insulin sensitivity and on the role of beta-cell function in glucose intolerance and diabetes.