Building Information Modelling (BIM) is a new process that is spreading in the Architecture, Engineering and Construction field. It allows the creation of virtual building models, which can be linked to numerical data, texts, images, and other types of information. Building components, such as walls, floors, etc. are modelled as "smart objects", i.e. they are defined by numerical parameters, such as dimensions, and are embedded with other kinds of information, such as building materials and properties. Stored data are accessible and modifiable by all different professionals involved in the same project. The BIM process has been developed for new buildings, and it allows to plan and manage the whole building life-cycle. BIM for built heritage has started to be researched recently, and its use is still not widespread. Indeed, built heritage is characterised by complex morphology and non-homogeneous features, which clash with BIM's standardised procedures. Moreover, to date, BIM does not allow fully automated procedures to model heritage buildings. This review focuses on the survey and digitisation phases, which can be seen as the initial phases of application of BIM in conservation projects. It also briefly covers the modelling stage. Here we present the main methodologies developed for BIM for built heritage. Issues about digitisation are also highlighted, principally in connection with the unavailability of automated processes. During the last 10 years, research has led to promising results; for example, videogame interfaces have been used to simulate virtual 3D tours that display in a single interface the 3D model and the database containing metadata, and new software plug-ins have been developed, to easily create "smart objects". Nevertheless, further research is needed to establish how BIM can support the practice of building conservation. There is a gap in BIM's information holding capacities, namely the storage of cultural and historical documentation, as well as monitored and simulated data relevant for preventive conservation. Future work should focus on the development of new tools that will be able to store and share all the relevant metadata.