In the building sector, concerns towards the vast energy consumption has promoted the development of renewable energy technologies. In this regards, the solar concentration devices show a promising concept for building applications. However, the solar concentrators for application in buildings have many restrictions, which are different from the traditional solar concentrators. The main objective of this paper is to present a concise review on the building integrated concentrating devices, that have their own characteristics and multiple functions. This paper made a classification based on device's functions, i.e. building integrated concentrated photovoltaic systems (BICPV), building integrated concentrating solar thermal (BICST) and building integrated concentrating solar daylighting (BICSD) and the combination of functions, i.e. BICPV/T, BICPV/D, BICST/D and BICPV/T/D. At the same time, this paper presented an elaborate introduction of the demands, types and applications of the building integrated concentrating devices and prospects/ directions/ policies about these technologies around the world. The review would provide important information for the actual engineering of building integrated concentrating devices.