The loss distribution approach (LDA) has evolved as the industry standard for operational risk models despite a number of known weaknesses. In particular, LDA’s traditional focus on historical loss data often neglects expert knowledge that is available for operational risk types of a more predictable nature. In this paper, we present an alternative quantification technique, so-called exposure-based operational risk (EBOR) models, which aim to replace historical severity curves by measures of current exposures and use event frequencies based on actual exposures instead of historical loss counts. We introduce a general mathematical framework for exposure-based modeling that is applicable to a large number of operational risk types. As an example, an EBOR model for litigation risk is presented. Further, we discuss the integration of EBOR and LDA models into hybrid frameworks facilitating the migration of operational risk subtypes from a classical to an exposure-based treatment. The implementation of EBOR models is a challenging task since new types of data and a higher degree of expert involvement are required. In return, EBOR models provide a transparent quantitative framework for combining forward-looking expert assessments, point-in- time data (eg, current portfolios) and historical loss experience. Individual loss events can be modeled in a granular way, which facilitates the reflection of loss-generating mechanisms and provides more reliable signals to risk management.