Since the first launch of an artificial satellite—Sputnik 1—in 1957, space activities have played a significant role as a pioneering technological sector with a high impact on the international scenario. The space system has changed rapidly in the last 30 years, as a result of an intersystemic transition from a bipolar and simplified space system in the 20th century to a new and more complex space system in the 21st century. The post-Cold War space system has undergone multiple changes in its key system parameters—actors, interactions, processes, trends, etc.—that require new scientific approaches. Currently, there is extensive literature that attempts to address these changes, but it is an atomized and fragmented approach that focuses only on particular aspects of space activities, failing to provide a holistic perspective of the systemic changes. This article is analytical and is concerned with how space activities can be empirically examined using a systemic-level approach and systems models, and how the fundaments of systems science are a valuable methodological toolkit to be applied to the field of space studies. Therefore, the main objective of this research is to apply a systems architecture model—previously developed for the author—to the study of the key characteristics of the 21st century space age. The result is a systemic-level study of the new space age in the 21st century, which identifies and describes the intersystemic transition from the Cold War (1947–1991) to the post-Cold War period (1991 to the present), showing the profound changes in the main parameters of the space system and the emergence of new space actors, interactions, processes, and megatrends in space that have a significant impact on the entire world system.