Today's organisations require techniques for automated transformation of the large data volumes they collect during their operations into operational knowledge. This requirement may be addressed by employing event recognition systems that detect activities/events of special significance within an organisation, given streams of 'low-level' information that is very difficult to be utilised by humans. Numerous event recognition systems have been proposed in the literature. Recognition systems with a logic-based representation of event structures, in particular, have been attracting considerable attention because, among others, they exhibit a formal, declarative semantics, they haven proven to be efficient and scalable, and they are supported by machine learning tools automating the construction and refinement of event structures. In this paper we review representative approaches of logic-based event recognition, and discuss open research issues of this field.