Geographic information science (GIScience) has been considered as a spatial science. Its focus therefore has been on handling spatial data. Our world however is more complex than static snapshots of various spatial distribution patterns. Things change over time and the observed spatial patterns often are the outcomes of various types of processes. In other words, we face a dynamic world that challenges the conventional GIS representation of map layers as static snapshots. Furthermore, human activities and interactions are increasingly expanding into virtual space enabled by modern information and communication technologies (ICT) such as the Internet and mobile phones in a mobile and connected world. It is no longer sufficient to only study activities and interactions in physical space if we want to gain a comprehensive understanding of modern societies. GIScience therefore should be able to represent, analyze and visualize activities and interactions in a hybrid physical-virtual space. This brings up some fundamental challenges of moving beyond the Cartesian coordinate system employed in conventional GIS to better integrate physical and virtual activities and interactions. Another important element missing in conventional GIS is persons. Although we may agree that human beings play a very active and important role in the world, conventional GIS often treat persons as passive attribute data associated with various locations rather than active, dynamic and mobile agents. This presentation discusses some challenges of developing Space, Time, and Person-based Geographic Information Science and uses a space-time GIS employing extended time-geographic concepts to illustrate some efforts of integrating space, time, and persons in a GIS environment.