Trust and monitoring are traditionally antithetical concepts. Describing trust as a property of a relationship of reliance, we introduce a theory of trust and monitoring, which uses mathematical models based on two classes of functions, including _q_-exponentials, and relates the levels of trust to the costs of monitoring. As opposed to several accounts of trust that attempt to identify the special ingredient of reliance and trust relationships, our theory characterizes trust as a quantitative property of certain relations of reliance that (...) can be quantified and expressed as a scalar quantity. Our theory is applicable to both human–human and human–artificial agent interactions, as it is agnostic with respect to the concrete realization of trustworthiness properties, and is compatible with many views differing on which properties contribute to trust and trustworthiness. Finally, as our mathematical models make the quantitative features of trust measurable, they provide empirical studies on trust with a rigorous methodology for its measurement. (shrink)