The underlying property, its definition and representation play a major role when monitoring a system. Having a suitable and convenient framework to express properties is thus a concern for runtime analysis. It is desirable to delineate in this framework the sets of properties for which runtime analysis approaches can be applied to. This paper presents a unified view of runtime verification and enforcement of properties in the Safety-Progress classification. Firstly, we extend the Safety-Progress classification of properties in a runtime context. Secondly, we characterize the set of properties which can be verified (monitorable properties) and enforced (enforceable properties) at runtime. We propose in particular an alternative definition of ''property monitoring'' to the one classically used in this context. Finally, for the delineated sets of properties, we define specialized verification and enforcement monitors.