In the ubicomp/percomp era, more ubiquitous computation/information/service would be the main driving force, and the corresponding essential element would be the various smart/intelligent ubiquitous things or u-things with attached/embedded/blended computers. Based on the soon available ubiquitous networking infrastructures and services, such ordinary u-things surrounding us are capable of computing, communicating, connecting or being connected, and behaving smartly with some intelligence. Our world would evolve towards a smart world mainly characterized by ubiquitous intelligence and filled with these smart u-things falling into three categories: smart object, smart space and smart system. The next research phase to emerge, we believe, is to coordinate these diverse smart objects and integrate these isolated smart spaces together into a higher level of spaces known as smart hyperspace or hyper-environments, and eventually create the smart world. In this paper, we discuss the potential trends and related challenges from smart things, smart spaces to smart hyperspaces toward the smart world with ubiquitous intelligence.