Abstract Words for numbers, numerals, are a special lexical class, halfway between natural and mathematical language. One would expect them to have a relatively straightforward semantics. However, during the last several decades, numerals proved to be a rich source of debate in linguistics, especially in semantics and pragmatics. The reason is that the study of numerals requires taking into account core issues such as plurality, quantification, implicature/exhaustivity, degree, modality, imprecision and cross‐linguistic variation. In this article, we provide a thorough introduction to the issues connected to numeral semantics and pragmatics. We gradually develop analyses of meanings of numerals in natural language using a multitude of analytical tools. We evaluate the competing proposals in terms of empirical coverage and predictions.