The shortening of product life-cycles accompanied by the rapid development of new products and dissolving industry boundaries are indicative of a multitude of potentially disruptive threats. The survival of incumbents depends on their capability to effectively anticipate and manage such threats. Thus, the early anticipation of disruptive threats to react or prepare for their impacts is a crucial topic in practice and academia. Although the current body of knowledge provides numerous approaches to disruption anticipation, a comprehensive conceptualisation of the evolution of disruptive threats is missing. Moreover, incumbents lack guidance on how to effectively anticipate disruptive threats. To address this gap, we propose the Disruption Evolution Framework (DEF), which conceptualises the course of disruptive threats along three phases (i.e. threat possible, apparent, and materialised) as well as distinguishes four interrelated categories of signals (i.e. context, catalyst, capability, and company signals) and threats (i.e. customer, competitor, product, and policy threats). Building on the DEF, we also propose the Disruptability Assessment Method (DAM), which enables incumbents to systematically assess disruptive threats via a step-by-step procedure. We evaluated the DAM in the Corporate Development and the Global Digital Partnerships departments of an insurance company. Overall, our work contributes to the descriptive and prescriptive knowledge on disruption anticipation.