Recent scientific and technological advancements driven by the Internet of Things (IoT), Machine Learning (ML) and Artificial Intelligence (AI), distributed computing and data communication technologies have opened up a vast range of opportunities in many scientific fields—spanning from fast, reliable and efficient data communication to large-scale cloud/edge computing and intelligent big data analytics. Technological innovations and developments in these areas have also enabled many opportunities in the space industry. The successful Mars landing of NASA’s Perseverance rover on 18 February 2021 represents another giant leap for humankind in space exploration. Emerging research and developments of connectivity and computing technologies in IoT for space/non-terrestrial environments is expected to yield significant benefits in the near future. This survey paper presents a broad overview of the area and provides a look-ahead of the opportunities made possible by IoT and space-based technologies. We first survey the current developments of IoT and space industry, and identify key challenges and opportunities in these areas. We then review the state-of-the-art and discuss future opportunities for IoT developments, deployment and integration to support future endeavors in space exploration.