A quantitative measure of wildfire risk across a landscape-expected net change in value of resources and assets exposed to wildfire-was established nearly a decade ago. Assessments made using that measure have been completed at spatial extents ranging from an individual county to the continental United States. The science of wildfire risk assessment and management continues to build on the basic framework to develop new analysis techniques that address specific fire management problems. This paper reviews central concepts of the basic risk assessment framework and describes several emerging terms and concepts now under development. These new concepts include: 1) describing certain results of stochastic simulation systems as a wildfire event set, 2) defining a biophysical fireshed as the land area where fires can originate and eventually reach a designated point, line or area in a designated period of time, 3) defining a fireplain as the land area where fire originating from a designated point, line or polygon (or set thereof) can reach during a designated period of time, 4) an exceedance probability curve, which plots the magnitude of an event (or its effects) against the likelihood that magnitude will be exceeded during a designated period of time, and 5) an analysis of wildfire Risk Associated with an Ignition Location (RAIL analysis), which characterizes the wildfire risk where the risk originates rather than where it occurs.