Today's information systems log vast amounts of data. These collections of data (implicitly) describe events (e.g. placing an order or taking a blood test) and, hence, provide information on the actual execution of business processes. The analysis of such data provides an excellent starting point for business process improvement. This is the realm of process mining, an area which has provided a repertoire of many analysis techniques. Despite the impressive capabilities of existing process mining algorithms, dealing with the abundance of data recorded by contemporary systems and devices remains a challenge. Of particular importance is the capability to guide the meaningful interpretation of 'oceans of data' by process analysts. To this end, insights from the field of visual analytics can be leveraged. This article proposes an approach where process states are reconstructed from event logs and visualised in succession, leading to an animated history of a process. This approach is customisable in how a process state, partially defined through a collection of activity instances, is visualised: one can select a map and specify a projection of events on this map based on the properties of the events. This paper describes a comprehensive implementation of the proposal. It was realised using the open-source process mining framework ProM. Moreover, this paper also reports on an evaluation of the approach conducted with Suncorp, one of Australia's largest insurance companies. [ABSTRACT FROM AUTHOR]