A cyber world (CW) is a digitized world created on cyberspaces inside computers interconnected by networks including the Internet. Following ubiquitous computers, sensors, e-tags, networks, information, services, etc., is a road towards a smart world (SW) created on both cyberspaces and real spaces. It is mainly characterized by ubiquitous intelligence or computational intelligence pervasion in the physical world filled with smart things. In recent years, many novel and imaginative researches have been conducted to try and experiment a variety of smart things including characteristic smart objects and specific smart spaces or environments as well as smart systems. 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 toward the smart world and ubiquitous intelligence from smart things to smart spaces and then to smart hyperspaces. Likewise, we show our efforts in developing a smart hyperspace of ubiquitous care for kids, called UbicKids.