The use of virtual labs in higher education is gaining growing interest, with different debates in the literature about their role in addressing learning outcomes and balancing hands-on activities. This study seeks to understand how labs can be virtualised and thus structured to contribute to engineering education, by adopting an innovative perspective in studying the labs themselves as core assets to be developed for teaching and learning. Following the precepts of grounded theory, we performed a multi-case study of nine labs that underwent a process of virtualisation and their role within three programs of engineering education. Findings revealed (1) the dynamics in uncovering and exploiting the potentialities of different virtualisation paths, by overcoming difficulties in funding or a wider use in different courses, (2) the structural needs, such as stakeholder collaboration specifics and technical update intensity, and (3) the importance of education and research specifics in driving the design and development of virtualised labs. The pattern analysis of the relation between these features guided the development of a typology of virtualised labs that can be ascribed to three structuring phases - identified as foundational, intermediate, and advanced - and constitute the key contribution of this paper for both theory and practice.