Not all properties are monitorable. This is a well-known fact, and it means there exist properties that cannot be fully verified at runtime. However, given a non-monitorable property, a monitor can still be synthesised, but it could end up in a state where no verdict will ever be concluded on the satisfaction (resp., violation) of the property. For this reason, non-monitorable properties are usually discarded. In this work, we carry out an in-depth analysis on monitorability, and how non-monitorable properties can still be partially verified. We present our theoretical results at a semantic level, without focusing on a specific formalism. Then, we show how our theory can be applied to achieve partial runtime verification of linear time properties expressed by concrete formalisms such as LTL.