Creating stories for exhibitions is a fascinating and in parallel laborious task. As every exhibition is designed to tell a story, museum curators are responsible for analyzing each exhibit in order to extract messages that form a story and position accordingly the objects in correct order within the museum space. In this context, we analyze how the technological advances in the fields of sensors and the Internet of Things can be utilized in order to construct a 'smart space', where exhibits can communicate with the visitors and to each other and can be organized automatically so that they can generate rich, personalized, coherent and highly stimulating experiences. We present the architecture of the system named 'exhiSTORY', that intends to provide the appropriate infrastructure to be used in museums and places where exhibitions are held, in order to support smart exhibits. We discuss and analyze the architecture of the system and the ways of its application in a cultural space.